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hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 amFollowed by: 2 members; Thanked: 9 times

by hey_thr67 » Fri May 18, 2012 1:53 am

When the sqare of a number and the cube of a smaller number are added the result is 593. If the square of the smaller number exceeds the bigger number by 55, find the difference of the two numbers.

A: 1
B: 2
C: 3
D: 4
E: 7

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Source: Beat The GMAT — Problem Solving | Fri May 18, 2012 1:53 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Fri May 18, 2012 2:23 am

hey_thr67 wrote:When the sqare of a number and the cube of a smaller number are added the result is 593. If the square of the smaller number exceeds the bigger number by 55, find the difference of the two numbers.

A: 1
B: 2
C: 3
D: 4
E: 7

Let A be the bigger number and a be the smaller number.

A^2 + a^3 = 593 -- (1)
a^2 - A = 55 -- (2)

The following values satisfy the second equation:
a = 8, A = 9 (we start with a = 8 because that is first square value that exceeds 55)
and
a = 9, A = 26
and so on.

a = 8, A = 9 satisfies the first equation also.
A - a = 1

[spoiler](A)[/spoiler] is correct.

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
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