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GMATPrep2 hard questions I could not answer correctly,>70 [#permalink]
06 Aug 2006, 17:40

Please see below the list of questions I could not answer on GMAT Prep2. I scored 770. I'm sure the score is inflated because I got lot of repeat questions. But I got to see how the 700 + level questions look like. Please post your explainations guy. I really appreciate it.

1) A certain list of 100 data has an avergae (arithmetic mean) of 6 and a standard deviation of d , where d is positive. Which of the following pairs of data when added to the list must result in a list of 102 data with standard deviation less than d ?

-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6

D.S
2) If ab not equal to 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane , is point (-x,y) in this same quadrant ?

1) xy > 0
2) ax > 0

3) During a trip on an expressway , Don drove a total of x miles , His avg speed on a certain 5-mile section of the expressway was 30 miles per hour and his avg speed for the remainder of the trip was 60 miles per hour . His travel time for the x-mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip ?

1. 8.5%
2. 50%
3. x/12%
4. 50/x%
5. 500/x%

D.S
4) If x not equal to y , is x-y/x+y > 1 ?
1. x > 0
2. y < 0

D.S
5) If m and r are two numbers on a number line , what is the value of r ?
1. The distance between r and 0 is 3 times the distance between m and 0.
2. 12 is halfway between m and r.

D.S
6) Is xy > 0 ?
1. x - y > -2
2. x - 2y < -6

D.S
7) Is sqrt((x-5)^2) = 5-x ?

1. -x|x| > 0

2. 5 - x > 0

D.S
8) If set S consists of the numbers 1,5,-2,8 and n , is 0<n<7 ?

1. THe median of the numbers in S is less than 5.
2. The median of the numbers in S is greater than

D.S
9) A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price . What was the store's gross profit on the 20 coats ?

1. If the selling price per coat had been twice as much , the store's gross profit on the 20 coats would have been $ 2400.
2. If the selling price per coat had been $2.00 more , the store gross's profit on the 20 coats would have been $440.

Thanks everyone !!! . I think I'm weak with Inequalities and tough Std. Deviation questions. I don't know exactly which strategy to apply for Inequalities ? Choosing nos or simplifying the stem... Any insight here will help.

It would have been easier for evereone to follow the discussion if you posted these questions separately, but anyway... By the way, some of these questions were already discussed on this forum

Let me try

1) A certain list of 100 data has an avergae (arithmetic mean) of 6 and a standard deviation of d , where d is positive. Which of the following pairs of data when added to the list must result in a list of 102 data with standard deviation less than d ?

-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6

The answer should be (E) (6 and 6). It follows from the definition of std. By adding 6s you don't change the mean, but std deviation is reduced

D.S
2) If ab not equal to 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane , is point (-x,y) in this same quadrant ?

1) xy > 0
2) ax > 0

I skipped this one

3) During a trip on an expressway , Don drove a total of x miles , His avg speed on a certain 5-mile section of the expressway was 30 miles per hour and his avg speed for the remainder of the trip was 60 miles per hour . His travel time for the x-mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip ?

x/60 - time to trave at constant 60 mph 5/30 + (x-5)/60 - time actually traveled

5/30 + (x-5)/60 = ... = (x+5)/60

Then you take the ratio of (x+5)/60 over x/60 to get to the answer

D.S
4) If x not equal to y , is x-y/x+y > 1 ?
1. x > 0
2. y < 0
(C)

I played with simple number x=1 and -1 and y=1 and -1

D.S
5) If m and r are two numbers on a number line , what is the value of r ?
1. The distance between r and 0 is 3 times the distance between m and 0.
2. 12 is halfway between m and r.

This one should be (E)

ST1. |r|=3|m|, Not suff

ST2. (m+r)/2=12 => m+r=24, Not suff

Combined, still not sufficient. Foe example, m=-12, r=36 and m=6 and r=18 both satisfy both conditions. So, not suff

D.S
6) Is xy > 0 ?
1. x - y > -2
2. x - 2y < -6

Not sure yet

D.S
7) Is sqrt((x-5)^2) = 5-x ?

1. -x|x| > 0

2. 5 - x > 0

(D)

ST1. -x|x|>0 => x<0 => SUFF ST2. 5-x>0 => SUFF

D.S
8) If set S consists of the numbers 1,5,-2,8 and n , is 0<n<7 ?

1. THe median of the numbers in S is less than 5.
2. The median of the numbers in S is greater than

The ST2 condition is incomplete?

D.S
9) A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price . What was the store's gross profit on the 20 coats ?

1. If the selling price per coat had been twice as much , the store's gross profit on the 20 coats would have been $ 2400.
2. If the selling price per coat had been $2.00 more , the store gross's profit on the 20 coats would have been $440.
(B)

Please clarify your answer for 1 and 7. I'm sorry for being a thick head , but :

in problem 1 , since we do not know the nos , how do we know that the mean will decrease.

in problem 7 , if x<0 lets say -5 , the sqrt((-10)^2)) != 10
since sqrt(100) can be + 10 or -10 ... So each statement no matter what the value of x is insuff...

ALso maybe I can learn from u guys , but when solving inequalities , how do I know when to apply numbers test like 1,-1, fraction , etc and when to simplify the stem ? For e.g , problem no 1 if you simplify the stem , then answer is different ...

in problem 1 , since we do not know the nos , how do we know that the mean will decrease.

Actually, if the mean will stay the same; it is the standard deviation that will decrease.

Let's denote the mean of of a set of n numbers (Xj) as M. Then, by definition,

M=sum(of Xj)/n => sum(of Xj)=M*n

Now, if we add 2 numbers to the set that both equal to M, te new mean of (n+2) numbers (let's call it M') is equal to

M' = (sum(of Xj) + M + M)/(n+2) = (M*n + M + M)/(n+2) = M(n+2)/(n+2) =M

So, we showed that the mean would not change.

Then, by definition of std, two new members of the set would bring 0 terms to the sum in the numerator, but the denominator is increased from n to n+2. So, the new ratio (std) must be less than the original std.

in problem 7 , if x<0 lets say -5 , the sqrt((-10)^2)) != 10
since sqrt(100) can be + 10 or -10 ... So each statement no matter what the value of x is insuff...

By definition, sqrt(x) is a positive number. So, sqrt(100)=10

Re: GMATPrep2 hard questions I could not answer correctly,&a [#permalink]
07 Aug 2006, 15:53

Giving these a shot

1) A certain list of 100 data has an avergae (arithmetic mean) of 6 and a standard deviation of d , where d is positive. Which of the following pairs of data when added to the list must result in a list of 102 data with standard deviation less than d ?

-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6

E ... This would not increase the numerator but increase the denominator i.e. SD = sqrt[{(x1-m)^2 + (x2-m)^2../n}]

D.S
2) If ab not equal to 0 and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane , is point (-x,y) in this same quadrant ?

1) xy > 0
2) ax > 0

Not sure

3) During a trip on an expressway , Don drove a total of x miles , His avg speed on a certain 5-mile section of the expressway was 30 miles per hour and his avg speed for the remainder of the trip was 60 miles per hour . His travel time for the x-mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip ?

D.S
4) If x not equal to y , is x-y/x+y > 1 ?
1. x > 0
2. y < 0

C

x>0 and y<0 i.e. x = m, y = -n (assume m, n are 2 postive numbers)

i.e. x-y/x+y = m+n/m-n which will be > 1

D.S
5) If m and r are two numbers on a number line , what is the value of r ?
1. The distance between r and 0 is 3 times the distance between m and 0.
2. 12 is halfway between m and r.

E again

ST1 = r = 3m or r = -3m
ST2 = r+m/2 = 12 i.e. r+m = 24

Combine both and you get => m =6 or m=12

D.S
6) Is xy > 0 ?
1. x - y > -2
2. x - 2y < -6

Got C

x-y>-2
-x+2y>6

Adding the two y>4 From 1 x>y-2 which means x>0
Hence both combined are sufficient

D.S
7) Is sqrt((x-5)^2) = 5-x ?

1. -x|x| > 0

2. 5 - x > 0

D

ST1 implies x<0, try any value and the equation holds
ST2 x<5, again try any value and it holds

D.S
8) If set S consists of the numbers 1,5,-2,8 and n , is 0<n<7 ?

1. THe median of the numbers in S is less than 5.
2. The median of the numbers in S is greater than

Question seems incomplete

D.S
9) A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price . What was the store's gross profit on the 20 coats ?

1. If the selling price per coat had been twice as much , the store's gross profit on the 20 coats would have been $ 2400.
2. If the selling price per coat had been $2.00 more , the store gross's profit on the 20 coats would have been $440.

B

Let s be the sale price per coat, c the cost and P total profit
P = 20(s-c)

ST1 20(2s-c) = 2P
Not sufficient

ST2 We know total coats are 20 hence increasing the price by 2 implies net profit increases by 2 * $20 = $40
Since new profit is $440 original profit was $440 - $40 = $400
SUFF

Thanks everyone !!! . I think I'm weak with Inequalities and tough Std. Deviation questions. I don't know exactly which strategy to apply for Inequalities ? Choosing nos or simplifying the stem... Any insight here will help.

3) During a trip on an expressway , Don drove a total of x miles , His avg speed on a certain 5-mile section of the expressway was 30 miles per hour and his avg speed for the remainder of the trip was 60 miles per hour . His travel time for the x-mile trip was what percent greater than it would have been if he had travelled at a constant rate of 60 miles per hour for the entire trip ?

1. 8.5% 2. 50% 3. x/12% 4. 50/x% 5. 500/x%

I did this by picking numbers (since I am algebraically challenged:)
If he was driving the whole trip at 65 miles an hour, it would take 65 minutes.However, if he drove the first 5 miles of it at 30 miles an hour, that is a mile every 2 minutes and that part of the trip takes 10 minutes
The rest of the trip would take exactly 60 minutes

Hence, we have a simple percentage problem, 70-65/65...

How would I translate that into the answer choice? I am sorry I am a little slow tonight. I have a headache