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

This topic has 1 expert reply and 1 member reply
AbdurRakib Junior | Next Rank: 30 Posts
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If the positive integer n is added to each of the integers 6

Post Sat Jun 18, 2016 12:33 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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,
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    Post 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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