Gmat prep qestions (help solve with strategies)

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Question 1
An architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public par, and workers who will be applying a finish to the exterior of the spheres need to know the surface area of each sphere. The finishing process costs $92/square meter. The surface area of a sphere is equal to 4Ï€r^2, where r is the radius of the sphere. What is the value that is closest of the cost of finishing a sphere with a 5.50 metre circumference as well as the cost of finishing a sphere with 7.85 meter circumference.
Options: $900, $1,200, $1,800, $2,800, $3,200 and $4,500.

Question 2
Six countries in a certain region sent a total of 75 representatives to an international congress and no two countries sent the same number of representatives. Of the six countries, A sent the second greatest number of representative. Did country A send at least 10 representatives?
1. One of the 6 countries sent 41 rep to the congress
2. Country A sent fewer than 12 rep to the congress

A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount what is the total fine for a book on the 4th day it is overdue.
$0.60, $0.70,$ 0.80, $0.90, or $1.00

Question 3
The sum of positive integers x and y is 77, what is the value of xy
1. X = y+1
2. X and y have the same tens digit
Question 4
Is x less than 20?
1. The sum of x and y is less than 20
2. Y is less than 20
Question 5
If xy + z = x(y+z) which of the following must be true

Question 6
If xy= 1, what is the value of 2 ^(x+y)^2/2 ^(x-y)^2
a) 2, b) 4, c) 8, d) 16, e)32
Question 7
In iscoselesces triangle RST what is the measure of angle R
1. The measure of angle T is 100 degree
2. The measure of of angle S is 40 degree
Question 8
Alice take home pay last year was the same each month and she saved the same fraction of her take home pay each month. The total amount of money that she has saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save,. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month.
½, 1/3, ¼, 1/5, 1/6,

Question 9
If x is a negative number, what is the value of x
1. X^2 = 1
2. X^2 + 3x + 2 =0
Question 10
Two water pumps working simultaneously at their respective constant rates took exactly 4 hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate
5hrs, 16/3, 11/2, 6, 20/3
Question 11
Of the students who eat in a certain cafeteria each student either likes or dislikes lima beans and each student either likes or dislikes Brussels sprouts. Of the students, 2/3 dislike lima beans and of those who dislike lima beans, 3/5 also dislike bruseels sprouts. How many of these students like Brussels sprouts but dislike lima beans.
1. 120 students eat in the cafeteria
2. 40 of the students like lima
Question 12
What is the average arithmetic mean of eleven consecutive integers
1. The average of the first nine integers is 7
2. The average of the last nine integers is 9
Question 13
On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line.
1. Xyz < 0
2. Xy < 0
Question 14
If a quality control check is made by inspecting a sample of 2 light bulbs from a box of 12 light bulbs, how many different samples can be chosen
6, 24, 36, 66, 72.

Question 15
Is w greater than 1?
1. W +2 > 0
2. W^2 > 1
Question 16
For a certain examination, a score of 58 was 2 standard deviation below the mean, and a score of 98 was 3 standard deviation above the mean. What was the mean score for the examination
74, 76, 78, 80, 82.

Question 17
In a certain deck of cards, each card has a particular integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be
3&15, 3&20, 4&13, 4&14, 5&14
Question 18
According to the directions on can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice.
25, 34, 50, 67 and 100.
Source: — Problem Solving |

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by anuprajan5 » Sat Oct 20, 2012 12:57 am
I'll give it a shot with the first 5. It would be helpful if each individual question came as a separate topic.

1. 2pi*r = 5.5 and 2pi*r = 7.85
squaring, 4pi^2*r^2 = 30.25 and 4pi^2*r^2 is almost 64
dividing by pi

4pi*r^2 almost 10 and 4pi*r^2 almost 20

Multiplying by 92$/sqm

first would be approximate 920 and the second approximately 1840

Check the options and you have A and C respectively

2.

Statement 1 - One of the 6 countries sent 41 reps

Taking slots the breakup could be 41 10 9 8 6 1 or 41 9 8 7 6 4. Therefore insufficient.

Statement 2 - Country A sent fewer than 12 rep to the congress
say A=11, we can have 30+11+10+9+8+7=75
say A=9, we can have 40+9+8+7+6+5=75

Combined, it doesnt say anything new. Hence E

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by anuprajan5 » Sat Oct 20, 2012 1:01 am
3.

1st day - 0.1
2nd day - 0.2 or 0.4 (double or addition)
3rd day - 0.4 or 0.5 (double or addition)
4th day - 0.8 or 0.7 (double or addition)

Answer B

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by anuprajan5 » Sat Oct 20, 2012 1:08 am
Question 3
The sum of positive integers x and y is 77, what is the value of xy
1. X = y+1
2. X and y have the same tens digit


Statement 1 -

This basically says that y and x are consecutive integers

y + y+1 = 77

Therefore y = 38 and x = 39. Sufficient

Statement 2 -

x and y have the same tens digit. This basically means that the numbers are close enough and add upto 77. This can only be possible if they are 38 and 39.

Another way of looking at this is

say 10a+b = y
and 10a+c = x

The reason why we took a as common is because both numbers have the same tens digit

20a+b+c = 77

This can be possible only if a is 3. If a were 2, then 20a = 40 and b and c would total to 37 which is not a plausible option.


Answer D

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by anuprajan5 » Sat Oct 20, 2012 1:11 am
Question 4
Is x less than 20?
1. The sum of x and y is less than 20
2. Y is less than 20

Statement 1 - Insufficient

x+y<20
25-6<20
14+5<20

x can be greater than 20 or less than 20

Statement 2 - Insufficient

y<20 - Does not give us any relationship with x.

Combined, does not tell us anything new. The cases in Statement 1 are applicable when combined as well. E

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by anuprajan5 » Sat Oct 20, 2012 1:15 am
Question 5 is incomplete

Question 6
If xy= 1, what is the value of 2 ^(x+y)^2/2 ^(x-y)^2
a) 2, b) 4, c) 8, d) 16, e)32

Answer D

This equation simplifies to 2^2xy/2^-2xy which translates to 4/(1/4) - since xy = 1. Therefore 16

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by anuprajan5 » Sat Oct 20, 2012 2:17 am
Question 7
In iscoselesces triangle RST what is the measure of angle R
1. The measure of angle T is 100 degree
2. The measure of of angle S is 40 degree

Answer is A

Statement 1 - There are 2 equal sides meaning that there are 2 equal angles.

Since the sum of angles is 180 degrees, there is no way angle T can be one of the equal angles. Therefore sufficient.

Statement 2 - The measure of angle S is 40 degrees.

We could have a combination of 40-40-100 or 40-70-70 as angles. Hence insufficient.

REgards
Anup

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by anuprajan5 » Sat Oct 20, 2012 2:21 am
Question 8
Alice take home pay last year was the same each month and she saved the same fraction of her take home pay each month. The total amount of money that she has saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save,. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month.
½, 1/3, ¼, 1/5, 1/6,


f - fraction
m - monthly take home

This equates to f*m*12=3(1-f)*m

12f= 3-3f

[spoiler]f = 1/5[/spoiler]

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by anuprajan5 » Sat Oct 20, 2012 2:23 am
Question 9
If x is a negative number, what is the value of x
1. X^2 = 1
2. X^2 + 3x + 2 =0

Statement 1 - The only solution is that x=-1

Sufficient

Statement 2 - This simplifies to (x+1)*(x+2) = 0

x = -1,-2. Insufficent

Answer A

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by Brent@GMATPrepNow » Sat Oct 20, 2012 6:51 am
In the future, please post only one question per thread.

As you might imagine, this thread would get very messy very quickly, if others started commenting on various questions.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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