Problem Solving

Q. Are X and Y both Positive?
1. 2X-2Y = 1
2. x/Y > 1

Ans: C


Q. For every positive even integer n, the function h(n) is defined to be the product of all the

even integers from 2 to n, inclusive. If P is the smallest prime factor of h(100) + 1 then P is

a. between 2 and 10
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
e. greater than 40 ( Ans )


Q. The number 75 can be written as the sum of the squares of 3 different positive integers. What

is the sum of these 3 integers?
17, 16, 15, 14, 13

Ans: 13


Q. To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables

from a collection of chairs and tables in a warehouse that are all different from each other.If

there are 5 chairs in the warehouse and if 150 different combinations are possible, howmany

tables are in the warehouse?

6,8,10, 15, 30

Ans : 6

Q. A manufacturer conducted a survey to determine how many people buy products P and Q. What

fraction of people surveyed said that they buy neither product P nor product Q?

1. 1/3 of the people surveyed said that they buy product P but not product Q.
2. 1/2 of the people surveyed said that they buy product Q.

Ans : C

just want to verify is the answer( neither ) = 1/6?


Q. If m>0 and n >0, is [(m+x)/(n+x) ] > m/n?
1. m < n
2. x > 0

Ans : C


Q. Martha bought an armchair and a cofee table at an auction and sold both item at her store.

HEr gross profit from the purchase and sale of the armchair was what percent greater than her

gorss profit from the purchase and sale of the cofee table?

1. Martha paid 10% more for the armchair than for the cofee table.
2. MArtha sold the armchair for 20% more than she sold the coffee table.

Ans : E

A1.)
Look at the first inequality, you can ascertain that either X and Y are both positive or X and Y are both negative.
Assuming they are negative:
Let X be -2 and Y be -3
-2/-3 is not greater than 1

Let X be -3 and Y be -2
-3/-2 is greater then 1

Substituting values in bold in equation 1
2x(-3) - 2x(-2)= -6 + 4 = -2.
therefore does not satisfy.

Hence, X and Y have to be positive to satisfy both the sufficiency's.
Hence, C.

A.3)
You can do this by trial and error methods of the squares of numbers.
I got 7^2 + 5^2 + 1^2 = 75
& 7+5+1=13

Logically thinking, the sum of the squares to add up to 75: 5^2 = 25 is surely needed now any 2 more numbers the squares of which add up to 50 .
You may try with different combinations of numbers from 1 TO 8 TO GET TO 75.