BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Sat Aug 23, 2014 11:19 pm
Location: Dhaka,Bangladesh
Thanked: 2 times
Followed by:1 members

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

by AbdurRakib » Sat Jun 18, 2016 12:33 am
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
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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]
Image
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 410
Joined: Fri Mar 13, 2015 3:36 am
Location: Worldwide
Thanked: 120 times
Followed by:8 members
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
Top
Post new topic Post Reply
• Page 1 of 1