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Register now and save up to $200 Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code If the positive integer n is added to each of the integers 6 This topic has 2 expert replies and 1 member reply AbdurRakib Junior | Next Rank: 30 Posts Joined 23 Aug 2014 Posted: 25 messages Followed by: 1 members Upvotes: 2 Target GMAT Score: 750+ If the positive integer n is added to each of the integers 6 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 Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! GMAT/MBA Expert Scott@TargetTestPrep GMAT Instructor Joined 25 Apr 2015 Posted: 548 messages Followed by: 3 members Upvotes: 43 Top Reply Fri Dec 08, 2017 7:29 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 We are given that the positive integer n is added to each of the integers 69, 94, and 121, and need to determine the value of n. Statement One Alone: 69 + n and 94 + n are the squares of two consecutive integers. From statement one, we can say that for some positive integer x, 69 + n = x^2 and 94 + n = (x + 1)^2. Letâ€™s subtract the first equation from the second equation: (94 + n) - (69 + n) = (x + 1)^2 - x^2 25 = x^2 + 2x + 1 - x^2 25 = 2x + 1 24 = 2x 12 = x Since we know x = 12, we can substitute this into the first equation to determine the value of n: 69 + n = 12^2 69 + n = 144 n = 75 Statement one alone is sufficient to answer the question. Eliminate answer choices B, C and E. Statement Two Alone: 94 + n and 121 + n are the squares of two consecutive integers. We can use the same method that we used in statement one to solve for n. Therefore, without performing the actual calculations, we can conclude that we can find a unique value for n. Statement two alone is also sufficient to answer the question. Answer: D _________________ Scott Woodbury Stewart Founder & CEO GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions 5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT OptimusPrep Master | Next Rank: 500 Posts Joined 13 Mar 2015 Posted: 410 messages Followed by: 7 members Upvotes: 120 GMAT Score: 770 Top Reply 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 _________________ Ankur 99th Percentile GMAT Tutor | Optimus Prepâ„¢ Optimus Prepâ„¢ GMAT Courses: www.Optimus-Prep.com/GMAT Free Online Trial Hour: http://www.optimus-prep.com/request-free-online-trial-hour/ Free GMAT Study Plan: http://www.optimus-prep.com/ebook/ Optimus Prepâ„¢ Rates: GMAT Private Tutoring Online:$80-100/hr.*
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Thanked by: Anaira Mitch

GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
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Posted:
548 messages
Followed by:
3 members
43
Fri Dec 08, 2017 7:29 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
We are given that the positive integer n is added to each of the integers 69, 94, and 121, and need to determine the value of n.

Statement One Alone:

69 + n and 94 + n are the squares of two consecutive integers.

From statement one, we can say that for some positive integer x, 69 + n = x^2 and 94 + n = (x + 1)^2. Letâ€™s subtract the first equation from the second equation:

(94 + n) - (69 + n) = (x + 1)^2 - x^2
25 = x^2 + 2x + 1 - x^2
25 = 2x + 1
24 = 2x
12 = x

Since we know x = 12, we can substitute this into the first equation to determine the value of n:

69 + n = 12^2
69 + n = 144
n = 75

Statement one alone is sufficient to answer the question. Eliminate answer choices B, C and E.

Statement Two Alone:

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

We can use the same method that we used in statement one to solve for n. Therefore, without performing the actual calculations, we can conclude that we can find a unique value for n. Statement two alone is also sufficient to answer the question.

_________________

Scott Woodbury Stewart Founder & CEO
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