## GRE Numeric Entry Sample Questions

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1. Question :

The product of two positive numbers is 300 and the sum of their squares is 25 more than two times their product.
Find the sum of the two numbers.

Explanation:

Let the numbers be x and y.

According to the given conditions, we have

xy=300

x^2+y^2=2xy+25

=2*300+25

=600+25=625

(x+y)^2=x^2+y^2+2xy

=625+2*300

=625+600=1225

x+y=sqrt(1225)

=35

The sum of the numbers is 35

2. Question :

The product of the digits of a two-digit number is 15 and the sum of the digits is 8. The digits interchange
their places when 18 is added to the number.

Find the number.

Explanation:

Let the digit in the units place be x and the one in the tens place be y.

The number will be 10y+x.

xy=15 and x+y=8

Putting x=8-y in xy=15, we get

(8-y)y=15

8y-y^2-15=0

y^2-8y+15=0

y^2-5y-3y+15=0

y(y-5)-3(y-5)=0

y=3,5

When y=3, x=5 and when y=5, x=3

The number is either 35 or 53.

When 18 is added to the number the digits interchange their places.

35+18=53

Hence, the number is 35.

3. Question :

The price of wheat has fallen by 10%. How many quintals can be purchased for the same price for which 27 quintals
could be bought before?

Explanation:

Let the price per quintal before be x.

Total cost of 27 quintals=27x

Reduction in price is 10%

New price=x-10x/100

=90x/100=0.9x

Number of quintals that can be purchased now=27x/0.9x

=30

30 quintals can be bought now.

## GRE Numeric Entry Sample Questions

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