Data Sufficiency

Can anyone help me answer the below DS questions? Thanks for the help.

1. On a certain day it took Bill three times as long to drive from home to work as it took Sue to drive from home to work. How many kilometers did Bill drive from home to work?
(1) Sue drove 10 kilometers from home to work, and the ratio of distance driven from home to work time to drive from home to work was the same for Bill and Sue that day.
(2) The ratio of distance driven from home to work time to drive from home to work for Sue that day was 64 kilometers per hour.

2. If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
(1) n is the cube of an integer.
(2) n is even.

3. Is x^2 – y^2 a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.

4. The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?
(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.

OA: 1-A ; 2-A ; 3-C ; 4-D

crackgmat007 wrote: 2. If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
(1) n is the cube of an integer.
(2) n is even.

From the question, we know that 2 < n < 100. We also know that n is a square of an integer. There are 8 possible values.

From statement 1, we know that n is also the cube of an integer. Only possible value that n can take is 64. 64 is the square of 8 and cube of 4.

Hence A.

crackgmat007 wrote: 3. Is x^2 – y^2 a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.

Statement 1. x - y is positive. i.e., x - y > 0
or x > y. If x is positive, then x + y > 0 and hence x^2 - y^2 will be positive. But x could be negative. In that case, x + y < 0 and x^2 - y^2 will be negative.

So, cannot determine using statement 1.

Statement 2. x + y is positive. x + y > 0 => x > -y. If x > -y, there are two possibilities x > y or x < y.
For instance, x = 2, y = 3. Then x > -y. But x < y
Conversely, x = 2, y = 1, Then x > -y. And x > y. Without knowing if x > y or not we cannot determine if x - y > 0 or x - y < 0.

Hence, we will not be able to say if x^2 - y^2 > 0.

Combining the two statements, if x - y > 0 and x + y > 0, then the product of the two numbers (x - y) (x + y) > 0.

Choice C

4. The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?
(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.

(1) Let X be the dimension of edge of square initially

(x-1)(x+2) = 70

from here (x+9)(x-8) = 0

so x = 8

hence initial area = 8^2 = 64

(2) (x+2) = 1.25(x)

x= 8

so, again area is 64

So we can use any of the sentence
Hence
D

3. Is x^2 – y^2 a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.

x^2 – y^2 = (x+y)(x-y)
for this to be more than 0

ie:(x+y)(x-y)> 0

either both the factors have to be positive or else both the factors have to be negative

as, (+ve)(+ve) >0
and (-ve)(-ve) > 0
eg: (-2)(-4) = 8 >0


So St I : does not give any information about the other factor

St II: same,: does not give any information about the other factor

But combine both

We get information about both the factors

Hope this is clear to you now

Karan

crackgmat007 wrote:1. On a certain day it took Bill three times as long to drive from home to work as it took Sue to drive from home to work. How many kilometers did Bill drive from home to work?
(1) Sue drove 10 kilometers from home to work, and the ratio of distance driven from home to work time to drive from home to work was the same for Bill and Sue that day.
(2) The ratio of distance driven from home to work time to drive from home to work for Sue that day was 64 kilometers per hour.

tb = 3ts db=?
1. db/tb = ds/ts = 10/ts
db/3ts = 10/ts or db = 30 Sufficient
2.only the ratio ds/ts is given =64/1 it can also be 128/2 etc.....so insufficient

Hence A