Collection of 12 DS questions : GMAT Data Sufficiency (DS)
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# Collection of 12 DS questions

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Math Expert
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Collection of 12 DS questions [#permalink]

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17 Oct 2009, 17:45
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New questions:

1. When the positive integer x is divided by 4, is the remainder equal to 3?
(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.

2. In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?
(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1.
(2) It sold each computer for $1000. 3. Last Tuesday a trucker paid$155.76, including 10 percent state and federal taxes, for diesel fuel. What was the price per gallon for the fuel if the taxes are excluded?
(1) The trucker paid $0.118 per gallon in state and federal taxes on the fuel last Tuesday. (2) The trucker purchased 120 gallons of the fuel last Tuesday. 4. What is the remainder when the positive integer x is divided by 8? (1) When x is divided by 12, the remainder is 5. (2) When x is divided by 18, the remainder is 11. 5. Al, Pablo, and Marsha shared the driving on a 1500 mile trip, which of the three drove the greatest distance on the trip? (1) Al drove 1 hour longer than Pablo but at an average of 5 miles per hour slower than Pablo. (2) Marsha drove 9 hours and averaged 50 miles per hour 6. How many perfect squares are less than the integer d? (1) 23 < d < 33 (2) 27 < d < 37 7. The integers m and p are such that 2 is less than m and m is less than p. Also, m is not a factor of p. If r is the remainder when p is divided by m, is r > 1. (1) The greatest common factor of m and p is 2. (2) The least common multiple of m and p is 30. 8. A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed? (1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells. (2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample. 9. Is x^2 equal to xy? (1) x^2 - y^2 = (x+5)(y-5) (2) x=y 10. A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket? (1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket. (2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket. 11. If p is a prime number greater than 2, what is the value of p? (1) There are a total of 100 prime numbers between 1 and p+1 (2) There are a total of p prime numbers between 1 and 3912. 12. If x is a positive integer, what is the least common multiple of x, 6, and 9? (1) The LCM of x and 6 is 30. (2) The LCM of x and 9 is 45. As always please share your way of thinking. OA's (answers) are given in this post: collection-of-12-ds-questions-85441-20.html#p642315 Also you can check new set of PS problems: new-set-of-good-ps-85440.html _________________ Math Expert Joined: 02 Sep 2009 Posts: 37154 Followers: 7277 Kudos [?]: 96860 [4] , given: 10808 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 23 Oct 2009, 17:21 4 This post received KUDOS Expert's post 2 This post was BOOKMARKED ANSWERS (OAs): As most of the problems was solved correctly, I'm posting only OAs. Please let me know if anyone needs any clarification. 1. When the positive integer x is divided by 4, is the remainder equal to 3? (1) When x/3 is divided by 2, the remainder is 1. (2) x is divisible by 5. Answer: E. 2. In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003? (1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1. (2) It sold each computer for$1000.

3. Last Tuesday a trucker paid $155.76, including 10 percent state and federal taxes, for diesel fuel. What was the price per gallon for the fuel if the taxes are excluded? (1) The trucker paid$0.118 per gallon in state and federal taxes on the fuel last Tuesday.
(2) The trucker purchased 120 gallons of the fuel last Tuesday.

4. What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

5. Al, Pablo, and Marsha shared the driving on a 1500 mile trip, which of the three drove the greatest distance on the trip?
(1) Al drove 1 hour longer than Pablo but at an average of 5 miles per hour slower than Pablo.
(2) Marsha drove 9 hours and averaged 50 miles per hour

6. How many perfect squares are less than the integer d?
(1) 23 < d < 33
(2) 27 < d < 37

7. The integers m and p are such that 2 is less than m and m is less than p. Also, m is not a factor of p. If r is the remainder when p is divided by m, is r > 1.
(1) The greatest common factor of m and p is 2.
(2) The least common multiple of m and p is 30.

8. A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?
(1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.
(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.

9. Is x^2 equal to xy?
(1) x^2 - y^2 = (x+5)(y-5)
(2) x=y

10. A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket?
(1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket.
(2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket.

11. If p is a prime number greater than 2, what is the value of p?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3912.

12. If x is a positive integer, what is the least common multiple of x, 6, and 9?
(1) The LCM of x and 6 is 30.
(2) The LCM of x and 9 is 45.

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Re: NEW SET of good DS(4) [#permalink]

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02 Nov 2009, 19:33
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Talinhuu wrote:
Hello.

I just wonder whether the question No.8 is A or C.

I got A. May anyone explain to me if C is the right answer?

thx

A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?
(1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.
(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.

This one is really tough.

Before considering the statements let's look at the stem:
A. Population doubles at constant intervals, but we don't know that intervals.
B. Experiment will end in 4 hours from now.
C. We don't know when bacteria divided last time, how many minutes ago.

(1) Population divided 2 hours ago and increased by 3750 cells. Note that this statement is talking that bacteria quadrupled during 2 hours before NOW. So, starting point 2 hours ago, end of experiment 4 hours from now. Total 6 hours.
This statement gives ONLY the following info:
A. population of bacteria TWO hours ago - 1250.
B. population of bacteria now - 5000.

But we still don't know the interval of division. It can be 45 min, meaning that bacteria divided second time 30 min ago OR it can be 1 hour, meaning that bacteria just divided. Not sufficient.

(2) An hour before the end of experiment bacteria will double 40.000. Clearly insufficient.

(1)+(2) We can conclude that in 5 hours (2 hours before now+3 hours from now) population of bacteria will increase from 1250 to 40.000, will divide 5 times, so interval is 1 hour. The population will contain 40.000*2=80.000 cells when the bacteria is destroyed. Sufficient.

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Re: NEW SET of good DS(4) [#permalink]

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17 Oct 2009, 18:57
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Bunuel wrote:
1. When the positive integer x is divided by 4, is the remainder equal to 3?

(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.

(1) (x/3) = 2k+1 where k is an integer
x = 6k + 3
x is an odd integer; so x/4 may or may not have 3 reminder. NSF..

(2) x = 5m where m, a positive integer, could be 1, 2, 3, 4, 5, 6, 7 and so on..
If m = 1 or 2, 4, 5, reminder is not 0.
If m = 3, reminder is 3 or 7. NSF..

From 1 and 2: 5m = 6k + 3
If m = 3, k = 2 and x = 15. Then reminder is 3.
If m = 9, k = 7 and x = 45. Then reminder is 1.
If m = 15, k = 12 and x = 75. Then reminder is 3.

E..
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Re: NEW SET of good DS(4) [#permalink]

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17 Oct 2009, 19:35
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GMAT TIGER wrote:
Bunuel wrote:
1. When the positive integer x is divided by 4, is the remainder equal to 3?

(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.

(1) (x/3)/2 = k+1 where k is an integer
x = 6k + 6
x is an even integer; so x/4 has never 3 reminder. Suff...

When x/3 is divided by 2, the remainder is 1, should be "translated" x/3=2k+1 --> x=6k+3 and not x=6k+6
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Re: NEW SET of good DS(4) [#permalink]

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19 Oct 2009, 06:51
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Bunuel wrote:
New questions:

1. When the positive integer x is divided by 4, is the remainder equal to 3?
(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.

statement 1:
==========
x must be divisible by 3 but not by 2.So x must be odd multiple of 3 like 9,15,21,27..etc. Nt suff

statement 2:
==========
x is perfectly divisible by 5. x can be 5,10,15 etc.When we take 5 the rem is 1 and for 10 we get 2 and for 15 we get 3.Nt suff

combining both we x = 15,45,75....Still nt suff

So I will go with option E
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Re: NEW SET of good DS(4) [#permalink]

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19 Oct 2009, 09:38
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Bunuel wrote:
New questions:

11. If p is a prime number greater than 2, what is the value of p?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3912.

Also you can check new set of PS problems: new-set-of-good-ps-85440.html

1) Sufficient ... you can figure out the 100th prime # (from 1 to p+1)
2) Sufficient... you can count how many prime #s are between 1 & 3912 and that is P

D
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Re: NEW SET of good DS(4) [#permalink]

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20 Oct 2009, 22:47
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scoregmat wrote:
9. Is x^2 equal to xy?
(1) x^2 - y^2 = (x+5)(y-5)
(2) x=y

1) x^2 - y^2 = x^2 - 25
=> - y^2 = -25...=> y^2 = 25....y = 5.....
Insuff...

2) x = y....Suff..

B...Is there some trap ?

highlighted part is incorrect. However the answer is correct
the equation in 1 is x^2 - y^2 = (x+5)(y-5) which is equal to
x^2 - y^2 = xy -5x +5y -25 ----eqn1
for x^2 = xy value of x and y needs to be same.
On taking values as +/-5 for both x and y we can show the statement to be insuff
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Re: NEW SET of good DS(4) [#permalink]

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21 Oct 2009, 14:53
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I'll try the ones that haven't been attempted -

4. What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.
: E
if x = 29, it satisfies both (1) and (2) and the remainder when divided by 8 is 5.
if x = 65, it also satisfies both (1) and (2) but the remainder when divided by 8 is 1.
So both are Insuff.

7. The integers m and p are such that 2 is less than m and m is less than p. Also, m is not a factor of p. If r is the remainder when p is divided by m, is r > 1.
(1) The greatest common factor of m and p is 2.
(2) The least common multiple of m and p is 30.
: A
(A) implies that both m and p are even since they have 2 as a common factor. If thats the case, and given that m is not a factor of p means that the remainder will never be 0 or 1 so r > 1. So (A) is suff

(B) says that LCM(m,p) = 30. If m=3 and p=10, r =1; but if m = 6, p = 10, r = 4. So (B) is Insuff

8. A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?
(1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.
(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.
: A - Need know at what intervals the population doubles.
A says that in 2 hours the population quadrupled so every hour it doubles. Also, say population was x when it got divided 2 hours ago, then at 2 hours population is 4x so increase is 3x = 3750. Solve for x and can find out what the population will be 4 hours from now. Hence Suff.

B only says that the population reached 40000 cells with one hour remaining and says nothing about the rate. Depending on the rate, population can multiply to different levels. Hence not suff.
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Re: NEW SET of good DS(4) [#permalink]

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23 Oct 2009, 04:12
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Thanks for excellent questions Bunuel. It's truly appreciated. Since I really need practice on DS I tried to do them all. Unquestionably, I'm going to be wrong on some of them - so I look forward to seeing your answers.

Bunuel wrote:
New questions:

1. When the positive integer x is divided by 4, is the remainder equal to 3?
(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.

2. In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?
(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the

ratio of 2:1.
(2) It sold each computer for $1000. 3. Last Tuesday a trucker paid$155.76, including 10 percent state and federal taxes, for diesel fuel. What was the price per

gallon for the fuel if the taxes are excluded?
(1) The trucker paid $0.118 per gallon in state and federal taxes on the fuel last Tuesday. (2) The trucker purchased 120 gallons of the fuel last Tuesday. 4. What is the remainder when the positive integer x is divided by 8? (1) When x is divided by 12, the remainder is 5. (2) When x is divided by 18, the remainder is 11. 5. Al, Pablo, and Marsha shared the driving on a 1500 mile trip, which of the three drove the greatest distance on the trip? (1) Al drove 1 hour longer than Pablo but at an average of 5 miles per hour slower than Pablo. (2) Marsha drove 9 hours and averaged 50 miles per hour 6. How many perfect squares are less than the integer d? (1) 23 < d < 33 (2) 27 < d < 37 7. The integers m and p are such that 2 is less than m and m is less than p. Also, m is not a factor of p. If r is the remainder when p is divided by m, is r > 1. (1) The greatest common factor of m and p is 2. (2) The least common multiple of m and p is 30. 8. A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed? (1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells. (2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample. 9. Is x^2 equal to xy? (1) x^2 - y^2 = (x+5)(y-5) (2) x=y 10. A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket? (1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket. (2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket. 11. If p is a prime number greater than 2, what is the value of p? (1) There are a total of 100 prime numbers between 1 and p+1 (2) There are a total of p prime numbers between 1 and 3912. 12. If x is a positive integer, what is the least common multiple of x, 6, and 9? (1) The LCM of x and 6 is 30. (2) The LCM of x and 9 is 45. As always please share your way of thinking. 1. A. (x/3)/2=k+1 <=> x=6k+3 <=> x= 9,15,21,... Plug in numbers: 9/4 gives remainder of 1, 15/4 gives remainder of 3 => Insufficient B. x/5 is an integer. Since x>0 that means that x=5k <=> x=5,10,15... Plug in numbers: 5/4 gives remainder of 1, 10/4 gives remainder of 2 => Insufficient C. Plug in numbers by finding mutual possible values for x, e.g.: 15, 45. 15/4 gives remainder of 3. 45/4 gives remainder of 1. => Insufficient So answer is E. 2. I have no idea what a gross revenue ratio is. Could someone tell me? 3. Lets formalize the information.The trucker paid a total of 155.76 including taxes of 10%, thus excluding taxes he paid 155.76/1.1 A. We are informed that the trucker paid$0.118 pr. gallon in taxes. Formalizing this
information we get that:
p*1.1 - p = $0.118 <=> p(1.1-1)=$0.118 <=> p= $0.118/0.1 = 1.18. To exclude taxes just divide by 1.18/1.1. Sufficient B. Formalize the information. We know the trucker paid a total of 155.76/1.1 excluding taxes. To get the price pr. gallon exluding taxes just divide by with 20. Sufficient Hence answer is D. 4. A. x/12 = k+5 <=> x=12k+60 <=> x=72, 84, 96,.... Plug in numbers: 72/8 gives a remainder of 0, 84/8 gives a remainder of 4. Insufficient B. x/18 = k+11 <=> x=18k+11 <=> x=29,47,65 Plug in numbers: 29/8 gives a remainder of 5, 47/8 gives a remainder of 1. Insufficient C. Since A will always be even while B will always be uneven and there are no mutual values. Insufficient Hence answer is E. 5.Remember the formula time*speed=distance <=> t*S=d A. We are only given relative information on two of the three drivers, hence Insufficient B. We are told that Marsha drives 9*50 = 450 < (1/3)*1500, so Marsha cannot have driven the longest distance. That leaves Al and Pablo and therefore this statement is Insufficient c. We know from (2) that Marsha cannot be the answer. The distance left is 1500-450 = 1050 miles. Moreover, we know from (1) that Al drove one hour longer than Pablo, 5 miles pr. hour slower. By formalizing information we have one equation in two unknowns which is Insufficient Answer is E. 6. A. Since there is a perfect square between 23 and 33 (25) the number of perfect squares cannot be determined. Insufficient B. Since there is a perfect square between 27 and 37 (26) the number of perfect squares cannot be determined. Insufficient C. Combining (1) and (2) we know that 27 < d < 33. There are no perfect squares in this interval and thus there are 5 perfect squares less than d (1, 4, 9, 16, 25). Sufficient So answer is C. 7. Formalize the information: 2 < m < p. p/m is not an integer. A. GCF of m and p is 2, implying they are even numbers. We know that m is not a factor of P. Plug in numbers: 6/4 gives remainder of 2, 6/10 gives remainder of 4. Insufficient B. LCM of m and p is 30. Break down 30 into its prime factors: 2,3,5. Since m < p and it is not a factor of p, it can be either 3, 5 implying that p can be 10 and 6. Plug in numbers: 10/3 gives a remainder of 1, 6/5 gives a remainder of 1. Thus the remainder r=1 and therefore r is not >1. Sufficient The answer is B. 8. We know that the population doubles at certain intervals and that it doubles (from an unknown quantity) at exactly 4 hours before being destroyed. A. We're told that the population has quadrupled in two hours. That means that the population has doubled 3 times in two hours and therefore it will double 6 times in 4 hours. Furthermore we are told that 4x - x = 3750, where x is population 2 hours ago <=> x=3750/3 = 1250. Thus the total population will be 1250*2^(3+6). Sufficient B. We cannot infer how frequent the population doubles using this information. Insufficient Answer is A. 9. Is x^2 equal to xy? (1) x^2 - y^2 = (x+5)(y-5) (2) x=y 9. Rewrite the expression X^2=xy <=> xx=xy <=> x=y, thus the question reduces to whether x=y. A. Rewrite (1): (x+y)(x-y) = (x+5)(y-5). This equation is solved for x=y=5, but not for x=y=0. Thus the information is insuficcient. B. Since the question reduced to whether x=y and we are told that x=y this is clearly Sufficient So answer is B. 10. Since there are 20 oranges to be distributed and all baskets contain one orange, there can be a maximum of 20 baskets. Furthermore since they are evenly distributed only these combinations (orange X baskets) remain: , 10*2, 5*4, 4*5, 2*10, and 1*20. A. This gives no additional information and is clearly Insufficient B. There can be either 20, 10, 5, or 4 baskets. Since there are 20 oranges there number of baskets can be doubled without problems for 10, 5 and 4 baskets. Thus there must be 20 baskets. Sufficient So answer is B. 11.Since P is a prime greater than 2 it must be odd. A. Since p+1 is even and >2 and thus is not a prime number, p must be the 99. (since we are excluding 2) prime number (have no idea what that is though). Sufficient B. Again this can be counted straightforward. Find out how many primes there are in the interval and subtract 1 (because of 2). Sufficient Answer is D. 12. The LCM of 6 and 9 is are both factors of 3, but e.g. 9 is not a factor of 2, so the LCM of 6 and 9 is 18. A. Since the LCM of x and 6 is 30, x must be a factor of 5. Thus the LCM is 18*5 = 90. Sufficient B. Since the LCM of x and 9 is 45, x must be a factor of 5. Thus the LCM is 18*5 = 90. Sufficient So answer is D. Intern Joined: 01 Oct 2009 Posts: 10 Followers: 1 Kudos [?]: 4 [1] , given: 16 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 02 Nov 2009, 01:02 1 This post received KUDOS Hello. I just wonder whether the question No.8 is A or C. I got A. May anyone explain to me if C is the right answer? thx Math Expert Joined: 02 Sep 2009 Posts: 37154 Followers: 7277 Kudos [?]: 96860 [1] , given: 10808 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 19 Dec 2009, 10:43 1 This post received KUDOS Expert's post chetan2u wrote: hi bunuel, it seems the OA have already been given.. however i differ on one ans..i.e. 8.. i feel A is sufficient... SI tells us that the cells doubled two hour back and now are four times, ... it means that cells have doubled twice ..x then 2x... then 4x so they are doubling once every hr.. (although the SII doesnt have to relate to SI..... but just to check if it doubles once every hr..... change in the no 4x-x=3750 ..x=1250 so str presently is 5000... after 1 hr 10000..2 hr-20000...3hr-40000.... that is what SII tells) not a part of sol although.. I think this one was the toughest. I've already given the solution for this one previously, so here it is: Before considering the statements let's look at the stem: A. Population doubles at constant intervals, but we don't know that intervals. B. Experiment will end in 4 hours from now. C. We don't know when bacteria divided last time, how many minutes ago. (1) Population divided 2 hours ago and increased by 3750 cells. Note that this statement is talking that bacteria quadrupled during 2 hours before NOW. So, starting point 2 hours ago, end of experiment 4 hours from now. Total 6 hours. This statement gives ONLY the following info: A. population of bacteria TWO hours ago - 1250. B. population of bacteria now - 5000. But we still don't know the interval of division. It can be 45 min, meaning that bacteria divided second time 30 min ago OR it can be 1 hour, meaning that bacteria just divided. Not sufficient. (2) An hour before the end of experiment bacteria will double 40.000. Clearly insufficient. (1)+(2) We can conclude that in 5 hours (2 hours before now+3 hours from now) population of bacteria will increase from 1250 to 40.000, will divide 5 times, so interval is 1 hour. The population will contain 40.000*2=80.000 cells when the bacteria is destroyed. Sufficient. Answer: C. The point is that from (1) we can not say what the interval of division is, hence it's not sufficient. Please, tell me if you find this explanation not convincing and I'll try to answer your doubts. _________________ Math Expert Joined: 02 Sep 2009 Posts: 37154 Followers: 7277 Kudos [?]: 96860 [1] , given: 10808 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 23 Jan 2010, 23:06 1 This post received KUDOS Expert's post tengguli wrote: Hey all, First poster here. Many thanks to Bunuel in collecting these tests and answers. I'm particularly stuck in understanding the question below: Bunuel wrote: 11. If p is a prime number greater than 2, what is the value of p? (1) There are a total of 100 prime numbers between 1 and p+1 (2) There are a total of p prime numbers between 1 and 3912. From the solutions in this thread, it's suggested that we can count the number of prime numbers between 1 and 3912. However, my understanding is that the statement p is a prime number greater than 2 means that the number of prime numbers between 1 and 3912 must be a prime number as well. Am I misunderstanding the question, or is the total prime number between 1 and 3912 is actually a prime number? Many thanks. Welcome to the club. Yes, your understanding is correct. In data sufficiency questions the stem and the statements are providing us with the TRUE information. Stem says p is a prime number. Statement (2) says that "here are a total of p prime numbers between 1 and 3912". So yes the # of primes between 1 and 3912 MUST be prime number itself. We don't know what number it is, but we can calculate it, hence we can calculate p, hence (2) is also sufficient. Hope it's clear. _________________ Manager Joined: 06 Aug 2010 Posts: 224 Location: Boston Followers: 3 Kudos [?]: 185 [1] , given: 5 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 21 Oct 2010, 09:31 1 This post received KUDOS Why is the answer to number 2 not A? Let c be the price of computers and p be the price of printers. We know that c = 5p. All we want is the ratio of the revenue of computers and the revenue of printers. From A, we know that in the first half of the year, the ratio of c:p was 3:2, so the ratio was 3c/2p = 15p/2p = 15:2. In the second half of the year, the ratio of c:p was 2:1, so 2c/p = 10p/p = 10:1. Then the total ratio is (15/2)/2 + (10/1)/2 = 15/4 + 20/4 = 35:4. Why is this wrong? Retired Moderator Joined: 02 Sep 2010 Posts: 805 Location: London Followers: 108 Kudos [?]: 974 [1] , given: 25 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 21 Oct 2010, 14:22 1 This post received KUDOS 2. In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003? (1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1. (2) It sold each computer for$1000.

TehJay wrote:
Why is the answer to number 2 not A?

Let c be the price of computers and p be the price of printers. We know that c = 5p. All we want is the ratio of the revenue of computers and the revenue of printers. From A, we know that in the first half of the year, the ratio of c:p was 3:2, so the ratio was 3c/2p = 15p/2p = 15:2. In the second half of the year, the ratio of c:p was 2:1, so 2c/p = 10p/p = 10:1. Then the total ratio is (15/2)/2 + (10/1)/2 = 15/4 + 20/4 = 35:4. Why is this wrong?

Whats wrong is you cannot just add the two ratios. Consider the two extreme cases :

Case 1 : First half they sell 3million computers and 2million printers. Second half they sell 2 computers and 1 printer. The final ratio will be pretty much 3:2

Case 2 : First half they sell 3 computers and 2 printers. Second half they sell 2million computers and 1million printers. The final ratio will be pretty much 2:1

To find the final ratio, you need to exactly how many were sold in each half.
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Re: NEW SET of good DS(4) [#permalink]

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03 Feb 2011, 12:22
1
KUDOS
These may be the lousy way to solve the questions, but this is how I attempted to solve the questions.

The answers may be incorrect. I didn't match them with OA.

********************************************************************************************************
New questions:

1. When the positive integer x is divided by 4, is the remainder equal to 3?
(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.

Soln:

Q: will "x/4" leave a remainder of 3?

(1) Rephrase: (x/3)/2= x/6 leaves remainder 1.

Values of x: 1,7,13,19
x%4 : 1,3 Remainder may be 3 or NOT 3. Not Sufficient.

(2) x%5 = 0
Values of x: 5,10,15
x%4 : 1,2,3 Remainder may be 3 or NOT 3. Not Sufficient.

Both:
Values of x: 25,55,85,115
x%4 : 1,1,1,3 Remainder may be 3 or NOT 3. Not Sufficient.

Ans: "E"

*********************************************************************
2. In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?
(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1.
(2) It sold each computer for $1000. Q: What is ratio of: (total money received by selling computers)/(total money received by selling printers) (1) It just talks about the ratio of number of computers sold. Doesn't talk about how much was it sold for. Not Sufficient. (2) How many computer and how about the printer!! Not sufficient. Both: Not sufficient Ans: "E" *************************************************************************** 3. Last Tuesday a trucker paid$155.76, including 10 percent state and federal taxes, for diesel fuel. What was the price per gallon for the fuel if the taxes are excluded?
(1) The trucker paid $0.118 per gallon in state and federal taxes on the fuel last Tuesday. (2) The trucker purchased 120 gallons of the fuel last Tuesday. 1.1x=155.76 x=(155.76/1.1) x- base price paid for the entire purchase of the fuel without any taxes- known value (155.76/(1.1*10)) paid in the taxes (1) (155.76/(1.1*10))/n=0.118 Number of gallons n can be found. Then x/n to find the price/gallon without taxes. Sufficient. (2) (155.76/20)*0.9 will be the price per gallon without taxes. Sufficient. Ans: "D" ************************************************************************** 4. What is the remainder when the positive integer x is divided by 8? (1) When x is divided by 12, the remainder is 5. (2) When x is divided by 18, the remainder is 11. Same approach as question 1. I couldn't find any shortcuts for this. 1. x -> 5,17,29,41,53,65 x%8 -> 5,1,5,1,5,1. Can be 1 or 5. Not sufficient. 2. x -> 11,29,47,65 x%8 -> 3,5,7,1 Can be many remainders. Not sufficient. Both: x -> 29,65 x%8 -> 5,1. Can be many remainders. Not sufficient. Ans: "E" **************************************************************** 5. Al, Pablo, and Marsha shared the driving on a 1500 mile trip, which of the three drove the greatest distance on the trip? (1) Al drove 1 hour longer than Pablo but at an average of 5 miles per hour slower than Pablo. (2) Marsha drove 9 hours and averaged 50 miles per hour Total distance: 1500 miles (1) Al: Drove some miles driving for t hours at k miles/hour of speed Pablo: Drove some miles for t-1 hours (K+5) miles/hour of speed Miles driven by Al: tk Miles driven by Pablo: (t-1)(k+5) Can't deduce anything beyond this. Not sufficient. (2) Marsha drove 9*50=450 miles So Al+Pablo drove=1050 Definitely, Marsha didn't drive the maximum. Because, Al or Pablo could have driven around 1049 miles alone. Even if equally, they must have driven 1050/2=525 each, which is > 450. Not sufficient. Both: Marsha drove 450 miles Al + Pablo drove 1050 miles tk + (t-1)(k+5) = 1050 We can't derive exactly who drove how much of distance. Not sufficient. Ans: "E" ******************************************************************** 6. How many perfect squares are less than the integer d? (1) 23 < d < 33 (2) 27 < d < 37 (1) d could be 24 or 26 if d=24. Number of Perfect squares less than 24: 1^2=1, 2^2=4, 3^2=9, 4^2=16 = 4 if d=26. Number of Perfect squares less than 26: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25 = 5 Not sufficient. (2) 27 < d < 37 d can be any integer from 28 to 36, inclusive. from 28 to 36; the number of perfect square less than the number will always be 5. if d=28. Number of Perfect squares less than 26: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25 = 5 if d=36. Number of Perfect squares less than 36: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25 = 5 The question is trying to trick us by saying less than rather than "less than equal to". We should not count 36 as the perfect square because 36 is not less than 36. It is equal to 36. Sufficient Ans: "B" ***************************************************************** 7. The integers m and p are such that 2 is less than m and m is less than p. Also, m is not a factor of p. If r is the remainder when p is divided by m, is r > 1. (1) The greatest common factor of m and p is 2. (2) The least common multiple of m and p is 30. (1) m and p must both be even since p is not a multiple of m, remainder can't be 0. Can it be 1. For the remainder to 1, p will have to be odd, which is not possible. So, the remainder will always be more than 1. Sufficient. (2) Possible values for m and p are 2,15 -> Remainder: 1 Ans: No 3,10 -> Remainder: 1 Ans: No 5,6 -> Remainder: 1 Ans: No It can't be 1,30 because 30 is a multiple of 1. Sufficient. Ans: "D" ****************************************************************************** 8. A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed? (1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells. (2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample. (1) We can infer that bacteria is doubling every 2 hours. So, 2x: two hours back 4x: now 4x-2x=3750 2x=3750 x=1875 r = 2 A = 1875 n = 4 A(5) = a*r^(n-1) or simply: 3750*2=now in 2 hours: 3750*2*2 in 4 hours: 3750*2*2*2 Sufficient 2) I am not too sure what this statement is trying to say. However, here's an abortive effort. Say, it is time=1:00PM now We have to consider the time until 1+4=5:00PM It is saying that from "t+4-1" or from 4:00PM to 5:00PM, the bacteria will grow from 20,000 to 40,000. This is kind of too straightforward to be true. In other words, it is(or is it) saying that bacteria's count will be 40,000 when scientist destroys the sample. Sufficient Ans: "D" **************************************************************************************** 9. Is x^2 equal to xy? (1) x^2 - y^2 = (x+5)(y-5) (2) x=y (1) Following values satisfy the equation. x=y=-5 x=y=5 Can't think of any other number. But, I feel this is a lame way to solve this even if this is true. Sufficient. (2) Sufficient. Ans: "D" *********************************************************************************************** 10. A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket? (1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket. (2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket. Possibilities basket<->oranges/basket 20<->1 1<->20 10<->2 2<->10 4<->5 5<->4 (1) Consider 20<->1 Basket halved: 10 Oranges doubled: 2 Consider 10<->2 Basket halved 5<->4 So answer could be 20 or 2. Not sufficient. (2) Means after doubling the basket count, it will be more than 20. Possible only in 20<->1 scenario. 1 oranges. Sufficient Ans: "B" ************************************************************************************************************* 11. If p is a prime number greater than 2, what is the value of p? (1) There are a total of 100 prime numbers between 1 and p+1 (2) There are a total of p prime numbers between 1 and 3912. (1) p is the hundredth prime number. Can be found. Sufficient. (2) The total number of prime numbers can be found between 1 and 3912. p will be that total. Sufficient. Ans: "D" ******************************************************************************* 12. If x is a positive integer, what is the least common multiple of x, 6, and 9? (1) The LCM of x and 6 is 30. (2) The LCM of x and 9 is 45. (1) x can be 5 or 30. LCM=90 for both 5,6,9 and 30,6,9. Sufficient. (2) x can be 5 or 45. LCM=90 for both 5,6,9 and 45,6,9. Sufficient. Ans: "D" Thanks to the author. **************************************************************************** As always please share your way of thinking. Also you can check new set of PS problems: new-set-of-good-ps-85440.html _________________ SVP Joined: 29 Aug 2007 Posts: 2492 Followers: 69 Kudos [?]: 749 [0], given: 19 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 17 Oct 2009, 19:18 Bunuel wrote: 4. What is the remainder when the positive integer x is divided by 8? (1) When x is divided by 12, the remainder is 5. (2) When x is divided by 18, the remainder is 11. (1) x = 12k+5 ........ k is an integer that could be 1 or 2 or so on........NSF (2) x = 18m+11 ........ m is an integer that could be 1 or 2 or so on......NSF 1 and 2: 12k + 5 = 18m + 11...............where k>m. 12k = 18m + 6 2k = 3m + 1 If k = 2, m = 1. x = 29 and reminder is 5. If k = 5, m = 3. x = 60 and r = 4 If k = 8, m = 5................. r = 0. NSF.. Thats E. _________________ Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html GT Manager Joined: 12 Oct 2009 Posts: 115 Followers: 2 Kudos [?]: 63 [0], given: 3 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 18 Oct 2009, 00:10 Bunuel wrote: GMAT TIGER wrote: Bunuel wrote: 1. When the positive integer x is divided by 4, is the remainder equal to 3? (1) When x/3 is divided by 2, the remainder is 1. (2) x is divisible by 5. (1) (x/3)/2 = k+1 where k is an integer x = 6k + 6 x is an even integer; so x/4 has never 3 reminder. Suff... When x/3 is divided by 2, the remainder is 1, should be "translated" x/3=2k+1 --> x=6k+3 and not x=6k+6 will go with E 1. we can take x = 63 then (x/3)/2 = 21/2 leaves remainder 1 and remainder from 63/4 is 3 if we take x=45 then (x/3)/2 = 15/2 leaves a remainder 1 and remainder from 45/4 is 1 hence insuff 2. if x is 15 then its divisible by 5 and remainder is 3 (15/4 = 3 is remainder) but if x = 30 then remainder is 2 (30/4 gives 2 as remainder and divisible by 5) if we take both then (x/3)/2 should give remainder 1 and x is divisible by 5 let x = 15 then it satisfies both the conditions and x/4 will leave remainder 3 let x= 45 then again both conditions are satisfied but x/4 will leave remainder 1 . Hence insuff Manager Joined: 12 Oct 2009 Posts: 115 Followers: 2 Kudos [?]: 63 [0], given: 3 Re: NEW SET of good DS(4) [#permalink] ### Show Tags 18 Oct 2009, 00:40 Bunuel wrote: New questions: 2. In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003? (1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1. (2) It sold each computer for$1000.

3. Last Tuesday a trucker paid $155.76, including 10 percent state and federal taxes, for diesel fuel. What was the price per gallon for the fuel if the taxes are excluded? (1) The trucker paid$0.118 per gallon in state and federal taxes on the fuel last Tuesday.
(2) The trucker purchased 120 gallons of the fuel last Tuesday.

Also you can check new set of PS problems: new-set-of-good-ps-85440.html

2. Let cost of printer be x then cost of computer is 5x
option 1 -
given Nc1/Np1 = 3/2 and Nc2/Np2 = 2/1 (Nc1,Nc2,Np1 and Np2 are number of computers and printers sold in first and second half of the year)
here we do not know the exact price nor the numbers in each of 6months.
the ratios can be any number
Hence insuff
option2- cost of computer is 1000 we can calculate price of printer to be 200 but no further info on the number of units sold. hence insuff

taking both we have cost of computer and printer and ratios as well . Let ratio for first half be 3x/2x and for second half be 2y/y. Taking this also we will not be able to determine the gross revenue.hence E

3.given with tax the trucker paid $155.76 . The value of diesel without tax will come out to be$ 141.6.
1. Let number of gallons purchased is N. Then we have
(10/100)*141.6 = 0.118 *N we get N =120.
from this we can calculate price per gallon without tax. hence suff
2. number of gallons is given as 120 and we can calculate price per gallon without tax. hence suff
Hence D
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Re: NEW SET of good DS(4) [#permalink]

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18 Oct 2009, 07:34
Bunuel wrote:
GMAT TIGER wrote:
Bunuel wrote:
1. When the positive integer x is divided by 4, is the remainder equal to 3?

(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.

(1) (x/3)/2 = k+1 where k is an integer
x = 6k + 6
x is an even integer; so x/4 has never 3 reminder. Suff...

When x/3 is divided by 2, the remainder is 1, should be "translated" x/3=2k+1 --> x=6k+3 and not x=6k+6

Updated................
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Re: NEW SET of good DS(4)   [#permalink] 18 Oct 2009, 07:34

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