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# Beginners Forum (Re-worked questions)

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28 Jul 2005, 09:56
ywilfred,

Since the thread is disrupted, and for good reasons, I just want to take the chance to thank you for posting up this sticky. These problems sound very familiar and I can absolutely picturing them appearing on GMAT, yet most of these problems are difficult enough for me to challenge myself to learn the underlying concept.

Anyways, this is definately a set well-put-together questions you have here. Thank you again. I'll delete this message in a couple days so you go on with your thread.
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30 Jul 2005, 15:59

ywilfred wrote:
A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance travelled

For this question, what I would do is to brute force the answer, instead of looking at the algebraic way of solving it. It's much faster, and doesn't require much manipulation with algebraic terms. But for the purpose of learning, we'll look at both ways.

Brute-Force:

1s - 4 ft
2s - 9 ft
3s - 14 ft
4s - 19 ft
5s - 24 ft
6s - 29 ft
7s - 34 ft
8s - 39 ft
9s - 44 ft
10s - 49 ft
11s - 54 ft

Total = 4 + 9 + 14 + 19 + 24 + 29 + 34 + 39 + 44 + 49 + 54 = 319 ft

Pros of brute-forcing

- Doesn't require much thought process. Just scribble and add

Cons of brute-forcing
- Error Prone, since adding up under time pressure can lead to mistakes

Algebraic Way:

We know for the first second, the rider travels 4 ft. Subsequent second, he travels 5 ft more than the previous second. From this, we know we're dealing with an arithmetic progression (A.P) where each term is (a+n)
(a = first term, n = arithmetic difference).

The sum of an arithmetic progression, S, is defined as:
S = n/2 + {2a + (n-1)d} -------(1)

where n is the number of terms
a is the first term
d is the difference

S = n/2 (a+l) -----------------(2)
where n is the number of terms
a = first term
l = last term

Since we only know n, a and d, we use equation (1).

S = 11/2 + {2(4) + (11-1)5} = 319 ft

Pros of using this method:
-You can quickly work out the sum for a large number of terms (e.g. Sum of a A.P with 1000 terms)

Cons of using this method:
- Need to be able to identify an A.P
- Need to be able to recall the formula
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12 Aug 2005, 08:59
raki_sg wrote:

ywilfred wrote:
A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance travelled

For this question, what I would do is to brute force the answer, instead of looking at the algebraic way of solving it. It's much faster, and doesn't require much manipulation with algebraic terms. But for the purpose of learning, we'll look at both ways.

Brute-Force:

1s - 4 ft
2s - 9 ft
3s - 14 ft
4s - 19 ft
5s - 24 ft
6s - 29 ft
7s - 34 ft
8s - 39 ft
9s - 44 ft
10s - 49 ft
11s - 54 ft

Total = 4 + 9 + 14 + 19 + 24 + 29 + 34 + 39 + 44 + 49 + 54 = 319 ft

Pros of brute-forcing

- Doesn't require much thought process. Just scribble and add

Cons of brute-forcing
- Error Prone, since adding up under time pressure can lead to mistakes

Algebraic Way:

We know for the first second, the rider travels 4 ft. Subsequent second, he travels 5 ft more than the previous second. From this, we know we're dealing with an arithmetic progression (A.P) where each term is (a+n)
(a = first term, n = arithmetic difference).

The sum of an arithmetic progression, S, is defined as:
S = n/2 + {2a + (n-1)d} -------(1)

where n is the number of terms
a is the first term
d is the difference

S = n/2 (a+l) -----------------(2)
where n is the number of terms
a = first term
l = last term

Since we only know n, a and d, we use equation (1).

S = 11/2 + {2(4) + (11-1)5} = 319 ft

Pros of using this method:
-You can quickly work out the sum for a large number of terms (e.g. Sum of a A.P with 1000 terms)

Cons of using this method:
- Need to be able to identify an A.P
- Need to be able to recall the formula

Ah yes, thanks for pointing that out. I will make the change soon. Having problems with the internet connection....
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12 Aug 2005, 09:01
tritium6 wrote:
ywilfred wrote:
Is pq positive?

(1) (p + q)^2 > (p - q)^2
(2) (p - q)^2 is positive

From (1), We have (p + q)^2 > (p - q)^2. This can be simplified to:

(p^2 + 2pq + q^2) > (p^2 - 2pq + q^2)
4pq > 0
pq > 0.

So (A) alone is sufficient.

From (2), we have (p - q)^2 is positive, but this is not sufficient the square of any operation is always positive.

I disagree with this answer because it doesn't account for if either p or q is 0. If p is 0, pq is not positive. Therefore you can never tell if pq is positive or 0. The answer is E.

We do not have to consider so much because we know p times q must be greater than 0, and hence p or q cannot be 0 by themselves.
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25 Aug 2005, 13:08
ywilfred wrote:
Town T has 20,000 residents, 60% of whom are female. what percentage of the residents were born in town T?

1. The number of female residents who were born in town t is twice the number of male residents who were NOT born in town T

2. The number of female residents who were NOT born in Town T is twice the number of female residents who were born in Town T

From the passage, we know T has 20,000 residents of which, 60% or (60/100)*20,000 = 12,000 are female, and 8,000 (20,000-12,000) are male.

We're asked what percentage of residents were born in town T. This would be found by (# of residents born in town T)/(# of residents in town T) * 100%. Since we already know the denominator, what the question is really asking is the number of residents born in town T.

From statement (1), we're told:

# of female residents born in town T = 2*(# of male residents not born in town T)
We do now have the value for both LHS and RHS, and so statement (1) is not sufficient.

Note: The question stem only gives us the total number of female and male residents, and never broke them down into those that were born in town T, and those that were born outside town T.

From statement (2), we're told:

# of female residents not born in town T = 2*(# of female residents born in town T)

Let's say the number of female residents who were born in town T is x, then the number of female residents who were not born in town T would be (12,000-x). We can now equate both LHS and RHS and solve for the number of female residents who were born in town T. However, this still does not answer the question as we're lacking a figure representing the number of male residents born in town T. So statement (2) alone is not sufficient.

Using both (1) and (2), we can now use the value we found in (2), to calculate the number of male residents who were not born in town T, and therefore find the number of male residents who were born in town T. This would allow us to answer the question, and so C is the answer.

I am not sure but look at this Men born in town =Mb Not born Mnb, Female Born Fb , not born = Fnb

Statement 1: Fb=2Mnb
Mb + Mnb=8000
Fb +Fnb = 12000

let us get Not born together: from 22nd eq.

2Mnb + Fnb = 12000 (If we keep that not born can be represented by x so)
3x=12000 ==>x=4000

mean 4000 men are not born and 8000 women are not borm in town T and hence A sould be sufficient by itself

Statement 2 is not sufficient and it female only equation.

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26 Aug 2005, 14:51
ywilfred wrote:
Three cheese balls with diameters 1, 2, 6 respectively. Now melt the threes balls into one big cheese balls. What is the diameter.

(125)^(1/3)
(225)^(1/3)
(545)^(1/3)
(675)^(1/3)
(235)^(1/3)

Melting the three cheese balls and molding them together into one cheese ball will have one thing common. The volume of the big cheese ball will be the combined volume of the three cheese balls. To solve this, we need to use the formula for the volume of a sphere = 4/3*pi*(r^3)

For the cheese ball with dimeter of 1, V = 4/3 * pi * (1/2)^3 = pi/6
For the cheese ball with diameter of 2, V = 4/3 * pi * (1^3) = 4pi/3
For the cheese ball with diamater of 6, V = 4/3 * pi * (3^3) = 36pi

The total volume is therefore pi/6 + 4pi/3 + 36pi = 75pi/2

If the diamater of the big cheese cake = D, then the radius = D/2
So 4/3 * pi * (D/2)^3 = 75pi/2
D^3 = 225
D = 225^(1/3)

Nice explanation, but I would like to add one little shortcut; if you will.

4/3 pi r^3 is common everywhere so why even bother to go into detail calculation

r^3= 1/2^3 + 2/2^3 +6/2^3 = 225/8

r= 1/2 (225)^1/3 so D= 225^1/3

Hope that will save some time there
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26 Aug 2005, 14:54
ywilfred wrote:
The price of postage stamps has increased 5 cents per year every year since 1990. If 10 stamps were purchased every year from 1998 to 2002, the total cost would be $35. How much did a stamp cost in 1995? A. 45 cents B. 35 cents C. 40 cents D. 48 cents E. 52 cents We're told the stamps increased by 5 cents every year since 1990. So, this is a Arithmetic Sequence, where the frist term is the cost of a stamp in 1990, which we will cal a. The arithmetic difference is the increase in price, which is 5 cents. Thus, the nth term (or the nth year) would be defined as a + (n-1)d For 1998, a stamp would cost a + (9-1)5 = (a + 40) cents (Note: use 9 as n since the 2008 is actually the ninth term) For 1999, a stamp would cost a + (10-1)5 = (a + 45) cents For 2000, a stamp would cost a + (11-1)5 = (a + 50) cents For 2001, a stamp would cost a + (12-1)5 = (a + 55) cents for 2002, a stamp would cost a + (13-1)5 = (a + 60) cents The cost of 10 stamps in 1998 would be (10a + 400) cents The cost of 10 stamps in 1999 would be (10a + 450) cents The cost of 10 stamps in 2000 would be (10a + 500) cents The cost of 10 stamps in 2001 would be (10a + 550) cents The cost of 10 stamps in 2002 would be (10a + 600) cents Thus, the total cost of the stamps between 1998 to 2002 = (50a + 2500) cents =$35 = 3500 cents
Solving for a gives us a = 20 cents

The cost of a stamp in 1995 = a + (6-1)5 = 20 + 25 = 45 cents

Another shortcut

1998 to 2002 (== 5 terms 98,99,00,01,02) and 10 stamps increased by 5 cents every year, so. 10x into 5 and 10(x+5) will result:

50x+500=3500 so x=60 cents in 1998 so 45 cents in 1995

HTH
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29 Aug 2005, 15:20
ywilfred wrote:
Is 8x = 16 + 2x ?

1) -3x is greater than or equal to -9
2) 2x is greater than or equal to 6

Simplifying the equation in the question gives, 8x = 16 + 2x => 6x = 16 => x = 8/3. So the question is asking is x = 8/3.

From statement 1), -3x >= -9 => x <= 3. So statement (1) is clearly not sufficient since x can be greater than 3, or any value below 3.

From statement 2), 2x >= 6 => x >= 3. Statement (2) is sufficient since we know x is at least 3 and there is therefore no way that x can be 8/3.

is not 8/3 less than 3. Of course is 8/3 is 2.666
I look at this way 6x=16
statement 1- x<=3 so if x=3 6x is not equal to 18 so answer is NO. for any value of x < or = 3 the answer si always going to be no and is sufficient. This is Yes or No question so either answer is sifficient.

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21 Oct 2005, 21:14
dsprob wrote:
for any value of x < or = 3 the answer si always going to be no and is sufficient. This is Yes or No question so either answer is sifficient.

Not correct. x<=3 means x could equal 8/3 and the answer would be yes, but if x takes other values the answer would be no. 1) is thus insufficient.
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05 Feb 2006, 14:25
This equation S = n/2 + {2a + (n-1)d}
should be S = n/2 {2a + (n-1)d}

ywilfred wrote:
A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance travelled

For this question, what I would do is to brute force the answer, instead of looking at the algebraic way of solving it. It's much faster, and doesn't require much manipulation with algebraic terms. But for the purpose of learning, we'll look at both ways.

Brute-Force:

1s - 4 ft
2s - 9 ft
3s - 14 ft
4s - 19 ft
5s - 24 ft
6s - 29 ft
7s - 34 ft
8s - 39 ft
9s - 44 ft
10s - 49 ft
11s - 54 ft

Total = 4 + 9 + 14 + 19 + 24 + 29 + 34 + 39 + 44 + 49 + 54 = 319 ft

Pros of brute-forcing

- Doesn't require much thought process. Just scribble and add

Cons of brute-forcing
- Error Prone, since adding up under time pressure can lead to mistakes

Algebraic Way:

We know for the first second, the rider travels 4 ft. Subsequent second, he travels 5 ft more than the previous second. From this, we know we're dealing with an arithmetic progression (A.P) where each term is (a+n)
(a = first term, n = arithmetic difference).

The sum of an arithmetic progression, S, is defined as:
S = n/2 + {2a + (n-1)d} -------(1)

where n is the number of terms
a is the first term
d is the difference

S = n/2 (a+l) -----------------(2)
where n is the number of terms
a = first term
l = last term

Since we only know n, a and d, we use equation (1).

S = 11/2 + {2(4) + (11-1)5} = 319 ft

Pros of using this method:
-You can quickly work out the sum for a large number of terms (e.g. Sum of a A.P with 1000 terms)

Cons of using this method:
- Need to be able to identify an A.P
- Need to be able to recall the formula
Quote:
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08 Feb 2006, 13:13
I'm confused. Does X represent the total amount of grams in mixture x? If so, does (100-x) represent total amount of grams in mixture y? And why do we use (100-x)?
Why isn't the mixture x and mixture y assumed to be 100g like mixture xy?

ywilfred wrote:
Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 30% ryegrass, what percentage of the weight of this mixture is X?

Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.
Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.

So we can now equate the parts of the ryegrass in the mixture as:

0.4X + 0.25(100-X) = 30
0.4X + 25 - 0.25X = 30
0.15X = 5
X = 5/0.15 = 500/15 = 100/3

So the weight of mixture X as a percentage of the weight of the mixture
= (weight of X/weight of mixture) * 100%
= (100/3)/100 * 100%
= 33%

** For most percentage problems, equating one value to 100 is very helpful for a quick solution.
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08 Feb 2006, 20:37
For the solution, I don't understand why we are subtracting and dividing by three. Can somebody explain it to me? Thanks!

ywilfred wrote:
For all real numbers v, the operation v* is defined by the equation v* = v - v/3 . If (v*)* = 8, what is the value of v.

Since v* = v - v/3,

(v*)* = (v - v/3) - (v - v/3)/3
= (3v-v)/3 - [(3v-v)/3]/3
= 2v/3 - (2v/3)/3
= 2v/3 - 2v/9
= (6v - 2v)/9
= 4v/9

We also know that (v*)* = 8, so (v*)* = 8 = 4v/9 and v = 18.
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14 Feb 2006, 13:44
It does look rather complicated and confusing doesn't it? It may help you a little bit by using a different letter. We know the definition of v*=v-v/3. We can say that x*=x-x/3.
Now let x=v*.
Substitute it back into the x* equation: x*=x-x/3=v*-v*/3.
Now we can substitute v*=v-v/3 into the equation:
x*=x-x/3=v*-v*/3=(v-v/3)-(v-v/3)/3
You can go from there and simplify the equation and get your answer.
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14 Feb 2006, 17:33
I think I got it ! Thanks a bunch.
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28 Apr 2006, 13:40
Quote:
What is the least value of the three digit integer y?

1) the sum of the three digits is 5
2) y is divisible by 5

From statement (1), we're told the sum of the three digits is 5. The least value will therefore be in the range of 100+. 104 should therefore be the smallest number. Statement (1) is sufficient.

From statement (2), were told y is divisible by 5. So the last digit should be either 0 or 5. So the number can either be 100 or 105. Since we're asked for the least value, therefore y has to be 100. Statement (2) is therefore sufficient.

Hi,
I'm new here, but can someone please explain this one. From the actual problem, we know the smallest values of a 3-digit number is 100.

Statement 1 says the sum of the 3 digits is 5. This could be 104, 113, 203, etc. None of these values gives 100.
Statement 2 says y is divisible by 5. well 100 is divisible by 5, but so is 105, 110, 115, 120. Also Insufficient.

I would have chosen E.. and obviously got it wrong but can someone please clarify. Thanks in advance.
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29 Apr 2006, 06:25
How much was spent for a certian amount of a fabric?

(1) The cost of the fabric was $15 per square yard. (2) An additional 6 square yards of fabric would have cost an additional$90.

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19 May 2006, 07:27
SandeepM05 wrote:
Quote:
What is the least value of the three digit integer y?

1) the sum of the three digits is 5
2) y is divisible by 5

From statement (1), we're told the sum of the three digits is 5. The least value will therefore be in the range of 100+. 104 should therefore be the smallest number. Statement (1) is sufficient.

From statement (2), were told y is divisible by 5. So the last digit should be either 0 or 5. So the number can either be 100 or 105. Since we're asked for the least value, therefore y has to be 100. Statement (2) is therefore sufficient.

Hi,
I'm new here, but can someone please explain this one. From the actual problem, we know the smallest values of a 3-digit number is 100.

Statement 1 says the sum of the 3 digits is 5. This could be 104, 113, 203, etc. None of these values gives 100.
Statement 2 says y is divisible by 5. well 100 is divisible by 5, but so is 105, 110, 115, 120. Also Insufficient.

I would have chosen E.. and obviously got it wrong but can someone please clarify. Thanks in advance.

The point is that only the least number was wanted. This is not likely a GMAT question though. From experience for answer D the two options should give you the same answer most of the time.
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19 May 2006, 07:29
andrecrompton wrote:
How much was spent for a certian amount of a fabric?

(1) The cost of the fabric was $15 per square yard. (2) An additional 6 square yards of fabric would have cost an additional$90.

We want to know total cost. (1) gives unit price but not the amount bought. (2) gives again unit price for the additional 6 square yards. Both are insufficient, in my opinion, and combined is still insufficient.
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10 Oct 2006, 06:35
i tried this way.
when taking both choices i.e., x>2y and x<y+2

we can write, 2y<x<y+2
so x lies in between 2y and y+2 for all x,y>0

from 2y<x<y+2
implies 2y<y+2
impliws y<2

hence we can answer the question that y is not more than 2.
hencechoice c.

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12 Oct 2006, 21:41
ywilfred wrote:
A leopard spots a deer from a distance of 200 meters. As the leopard starts chasing the deer, the deer also starts running. Given that the speed of the deer is 10 km/h and that of the leopard is 12 km/h, how far would have the deer run before it is caught?

A. 3 km
B. 4 km
C. 2 km
D. 1 km
E. 5 km

This question test the ability to recall the Distance-Speed-Time formula, and also to manipulate the question to formulate the equation for solving the question (by use of algebra).
In such Distance-Speed-Time question (which involves A catching up with B), there's normally one quantity that's similar.
Also, remember to make sure that your units match, otherwise your answer will not come out right.

We know from the passage:
1. The Leopard and the Deer are 200 meters apart = 0.2 km
2. THe speed of the Leopard = 12km/hr
3. The speed of the Deer = 10 km/hr

Let's assume that the Deer has travelled x km before it is caught. The Leopard would then have to travel (x+0.2)km. There is one quantity that is the same here, that is the time taken for the deer to travel that x km, and for the Leopard to travel (x+0.2km).

Since we know that Time = Distance/Speed, we can equate:

Time taken by Deer to travel x km = Time taken by Leopard to travel (x+0.2) km
x/10 = (x+0.2)/12
12x = 10x + 2
2x = 2
x = 1 km

The differential distance of 2 km is being covered in 1hr. So, 0.2 km would be covered in 0.1 hr. And the deer will travel 1 km in 0.1 hr @ 10km/hr.
12 Oct 2006, 21:41

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