If the positive integer n is added to each of the integers 6

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AbdurRakib: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Sat Aug 23, 2014 11:19 pmFollowed by: 1 member; Location: Dhaka,Bangladesh; Thanked: 2 times

by AbdurRakib » Sat Jun 18, 2016 12:33 am

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If the positive integer n is added to each of the integers 69, 94, and 121, what is the value of n?

(1) 69 + n and 94 + n are the squares of two consecutive integers
(2) 94 + n and 121 + n are the squares of two consecutive integers

OG question new

Please explain the Answer

I didn't get the right approach to answer this question quickly

Thanks
Correct Answer D

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Source: Beat The GMAT — Data Sufficiency | Sat Jun 18, 2016 12:33 am

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by [email protected] » Sat Jun 18, 2016 8:26 am

Hi AbdurRakib,

This question is built around some Number Property logic and requires a bit of 'brute force' to get to the correct answer quickly.

We're told that N is a positive integer. We're asked for the value of N.

(1) 69 + n and 94 + n are the squares of two consecutive integers

This Fact tells us that (69+N) and (94+N) are two CONSECUTIVE PERFECT SQUARES. I'm going to list out some perfect squares so that we can look for a pattern:

1
4
9
16
25
36

Notice as you go down the list that the difference between any two consecutive squares INCREASES (that's the Number Property pattern I referenced earlier). The two numbers that we're told to consider differ by 25 (since 94-69 = 25), so we're looking for two consecutive squares that differ by 25. From the above pattern, we know that there will be JUST ONE pair that differ by 25 (the pairs that come before it will differ by less than 25 and the pairs that come after it will differ by more than 25) - whether we define it or not.

For the record, the numbers are 144 and 169, which makes X=75.
Fact 1 is SUFFICIENT

2) 94 + n and 121 + n are the squares of two consecutive integers.

The same logic that applies to Fact 1 applies to Fact 2, so we don't have to do any more work here.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Sun Jun 19, 2016 3:05 am

AbdurRakib wrote:If the positive integer n is added to each of the integers 69, 94, and 121, what is the value of n?

(1) 69 + n and 94 + n are the squares of two consecutive integers
(2) 94 + n and 121 + n are the squares of two consecutive integers

OG question new

Please explain the Answer

I didn't get the right approach to answer this question quickly

Thanks
Correct Answer D

Given: n is added to each of the integers 69, 94, and 121
Required: Value of n

Statement 1: 69 + n and 94 + n are the squares of two consecutive integers
The difference between the numbers = 94 - 69 = 25
Let us list down some of the perfect squares.
Since 69 is near to 8^2, I will start from 8^2

64, 81, 100, 121, 144, 169, 196, 225.

Difference between 169 and 144 = 25
Hence 94 + n = 169, and 69 + n = 144

n = 75
SUFFICIENT

Statement 2: 94 + n and 121 + n are the squares of two consecutive integers
Difference between the two = 121 - 94 = 27
Applying the same logic and writing the perfect squares.

100, 121, 144, 169, 196, 225

Hence the numbers are 196 and 169
121 + n = 196 and 94 + n = 169
n = 75
SUFFICIENT

Correct Option: D

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