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.
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)
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.
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.
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.
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)
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,
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.