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# Problem Solving and Data Sufficiency

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Problem Solving and Data Sufficiency [#permalink]  22 Jan 2008, 08:41
Hello, can somebody please explain how to solve the following questions. Thank you very much.

1. (1/5)^m * (1/4)^18 = 1/(2(10)^35), the correct answer is 35.

2. For all positive integers,[m]=3m when m is odd and[m]=m/2 when m is even. What is [9]*[6]? The correct answer is 27, but I got 81.

3. For the students in class A, the range of their heights is r centimeters and the greatest height is g centimeters. For the students in class B, the range of their heights is s centimeters and the greatest height is h centimeters. Is the least height of the students in class A greater than the least height of the students in class B?
(i) r < s
(ii) g > h

The answer is (c)-BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

4. Are X and Y both positive?
(1) 2X - 2Y = 1
(2) X/Y>1

The answer is (c)-BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

5. On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.

The answer is (c)-BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Thank you very much for your help.
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Re: Problem Solving and Data Sufficiency [#permalink]  22 Jan 2008, 10:58

1. (1/5)^m * (1/4)^18 = 1/(2(10)^35), the correct answer is 35.

On the left hand side (LHS), we have (1/5)^m multiplied by (1/4)^18 which can also be written as (1/2)^36, also as 1/2 * (1/2)^35.
Hence LHS is (1/5)^m * 1/2 * (1/2)35

On the right hand side (RHS), we have 1/2 * (1/10)35 = 1/2 * (1/5)35 * (1/2)35
Equating LHS and RHS, 1/2 * (1/2)35 cancels out and leaves us with (1/5)^m = (1/5)^35.
Hence m = 35

2. Based on the information given, the correct answer should be 81 and not 27. It should be a typo.

3. 1st statement: The range of A is less than the range of B. i.e the difference between the greatest and least heights is more for B than for A.
2nd statement: The greatest height of A is more than the greatest height of B.
Now putting the two statements together, the least height of A should be more than the least height of B, as the range for A is less than the range for B.

I would mark it to be C.

4. 1st statement : X - Y = 1/2 (E.g X = 3/4, Y = 1/4 OR X = 1/4, Y = -1/4 OR X = -1/4, Y = -3/4)
2nd statement : X > Y ( E.g X = -2, Y = -4 OR X = 4, Y = 2 OR X = 4, Y = -2 OR X = 1/4, Y = -1/4 OR X = 3/4, Y = 1/4 OR X = -1/4, Y = -3/4)

Both the statements are ambiguous. Putting them together, also doesn't tell if X and Y are both positive.
I would mark it to be E.

5. 1st statement helps us in getting the ratio of women to men ( W/C = 5/2, C/M = 5/11. Multiply W/C by 5/5 = 25/10. Multiply C/M by 2/2 will make it 10/22, hence W/M = 25/22)
2nd statement just tells that W is less than 30, it can be anything. Doesn't help in identifying the total # of people.
I would mark it to be E again.
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Re: Problem Solving and Data Sufficiency [#permalink]  23 Jan 2008, 09:51
Q.4
Statement I: 2x-2y=1
x-y=1/2
x=1/2+y.....(a)
Statement II: x/y>1
using eq. (a) above
1/2+y
-------- >1
y

1/(2y) + 1 >1
1/(2y) >0
Therefore y<0 ........( change of sign because of y moved from denominator to numerator)
This means y is (-) ve.
Statement II states that x/y is greater than 1 (that means +ve). For this to be true x must be negative..

Q.5
Given: W:C = 5:2

Statement I : C:M = 2:11
using given and statment I, we can find common ratio of W:C:M is 25:10:22
Statement II: No. of women is less than 30
this means no. of women is 25
therefore no. of men is 22
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Re: Problem Solving and Data Sufficiency [#permalink]  23 Jan 2008, 10:49
Q 4:

1) 2x-2y=1

Then 2(x-y)=1 or (x-y)=.5

We can have positive and negative numbers as well:

If x=1 and y=O.5, both are positive but we can have

If x=0.25 and y=-0,25.

So NO SUF

2)x/y>1 Then we can have both x and y positive or both negative. NO SUFICIENT

But together I and II, we have all the information.

So C
Re: Problem Solving and Data Sufficiency   [#permalink] 23 Jan 2008, 10:49
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