Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50039

If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
16 Jun 2016, 05:41
Question Stats:
76% (02:17) correct 24% (02:34) wrong based on 1087 sessions
HideShow timer Statistics




Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3907
Location: United States (CA)

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
08 Dec 2016, 09:55
Bunuel 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. Let’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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Manager
Joined: 21 Sep 2015
Posts: 78
Location: India
GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41

If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
Updated on: 03 Aug 2016, 09:44
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 Difference between the two squares is 25 since 9469=25. This difference is unique. For example 4^2  3^2 = 7 5^2 4^2 = 9 As can be seen the difference goes on increasing and hence only one unique value is possible. SUFFICIENT (2) 94 + n and 121 + n are the squares of two consecutive integers Difference between the squares is 27. Again this difference is unique . SUFFICIENT. (For those wondering what n is ; n=75 and the consecutive integeres are 12, 13 & 14)
_________________
Appreciate any KUDOS given !
Originally posted by rishi02 on 16 Jun 2016, 06:31.
Last edited by rishi02 on 03 Aug 2016, 09:44, edited 1 time in total.




Intern
Joined: 16 Jul 2014
Posts: 19
Location: United Arab Emirates

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
17 Jun 2016, 23:56
Let x and y be 2 consecutive squares such that y>x. Then root(y) = root (x) + 1 Now let's look at the question. 1) 94 + n and 69 + n are consecutive sqaures x = 69 + n y = 94+ n root(y) = root (x) + 1 Squaring the above equation we get: y = × + 2root (×) +1 2root (×) = y  x  1 = 94 + n  69  n  1 = 24 Root (x) = 12 x= 144 n = 144  69 = 75 y= 94 + 75 = 169 Sufficient 2) 94 + n and 121 + n are consecutive squares. Sufficient. Can be proven the same way as case 1.
_________________
KUDOS is great way to help those who have helped you.
THE KILL SET  700 level Sets quetions



Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 542
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
18 Jun 2016, 01:12
rishi02 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
Difference between the two squares is 25 since 9469=25. This difference is unique. For example 4^2  3^2 = 7 5^2 4^2 = 9
As can be seen the difference goes on increasing and hence only one unique value is possible. SUFFICIENT
(2) 94 + n and 121 + n are the squares of two consecutive integers
Difference between the squares is 27. Again this difference is unique . SUFFICIENT.
(For those wondering what n is ; n=75 and the consecutive integeres are 12, 13 & 14) Interesting application. Can you elaborate the highlighted Concept ? Thanks
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges



Manager
Joined: 21 Sep 2015
Posts: 78
Location: India
GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
18 Jun 2016, 01:57
AbdurRakib4^2  3^2 = 7 5^2 4^2 = 9 6^2 5^2 =11 100^299^2 = 199 The difference between the squares of consecutive integers always increases since a^2 b^2 = (a+b)(ab) (ab) will always be 1 since consecutive integers so as the integers increase a + b will also increase What you can also figure out from this is that a+b = 25 for this problem Therefore 2a +1 =25 and a =12 However you do not need to do this for a DS problem. Its sufficient to know that the difference is unique Hope its clear !
_________________
Appreciate any KUDOS given !



Senior Manager
Joined: 02 Dec 2014
Posts: 385
Location: Russian Federation
Concentration: General Management, Economics
WE: Sales (Telecommunications)

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
18 Jun 2016, 07:41
Bunuel 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 Statement 1. Let x and (x+1) be two consecutive integers. Then we have: 69+n=x^2 and 94+n=(x+1)^2. Substitute (69+n) into second equation to get 25+x^2=x^2 + 2x + 1 ==> 2x=24 and x=12 Hence n=75 Sufficient Statement 2. The same as Statement 1. Sufficient
_________________
"Are you gangsters?"  "No we are Russians!"



SVP
Joined: 06 Nov 2014
Posts: 1883

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
19 Jun 2016, 04:06
Bunuel 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 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



Senior Manager
Joined: 11 Nov 2014
Posts: 335
Location: India
Concentration: Finance, International Business
WE: Project Management (Telecommunications)

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
03 Aug 2016, 09:42
Good approach?
we know n>0 n is an integer
S1 (n69)(n94)=n*n*(n+1)*(n+1) (n69)(n94)=n^2*(n+1)*(n+1)
one variable, solved
same with S2
D



Manager
Joined: 30 Dec 2015
Posts: 86
GPA: 3.92
WE: Engineering (Aerospace and Defense)

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
29 Oct 2016, 19:40
AbdurRakib wrote: rishi02 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
Difference between the two squares is 25 since 9469=25. This difference is unique. For example 4^2  3^2 = 7 5^2 4^2 = 9
As can be seen the difference goes on increasing and hence only one unique value is possible. SUFFICIENT
(2) 94 + n and 121 + n are the squares of two consecutive integers
Difference between the squares is 27. Again this difference is unique . SUFFICIENT.
(For those wondering what n is ; n=75 and the consecutive integeres are 12, 13 & 14) Interesting application. Can you elaborate the highlighted Concept ? Thanks the BIG IDEA here: The difference between squares of two consecutive integers = Sum of the two consecutive integers eg: \(10^2  9^2 = (10+9)(109) = 19\) so on and so forth In Statement 1 we are told that (69+n) & (94+n) are the squares of two consecutive integers, So use the above idea: \((94+n)(69+n) = 25\) Since we know that the sum of the two consecutive integers is 25 & to find the individual consecutive integers: 25 = 2n+1 (since integers are consecutive) n = 12 & (n+1) = 13 Now that we have each individual integer: \(12^2 = (69+n)\) \(144 = 69 + n\) \(n = 75\) Same applies for statement 2
_________________
If you analyze enough data, you can predict the future.....its calculating probability, nothing more!



Intern
Joined: 19 Sep 2016
Posts: 1
Location: Panama
GPA: 3.98

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
03 Jun 2017, 17:33
ScottTargetTestPrep wrote: Bunuel 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. Let’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 ScottTargetTestPrep, Could you please explain why did you subtract 69 + n = x^2 and 94 + n = (x + 1)^2 ? Thank you.



Director
Joined: 09 Mar 2016
Posts: 946

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
16 Aug 2018, 09:31
colorblind wrote: AbdurRakib wrote: rishi02 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
Difference between the two squares is 25 since 9469=25. This difference is unique. For example 4^2  3^2 = 7 5^2 4^2 = 9
As can be seen the difference goes on increasing and hence only one unique value is possible. SUFFICIENT
(2) 94 + n and 121 + n are the squares of two consecutive integers
Difference between the squares is 27. Again this difference is unique . SUFFICIENT.
(For those wondering what n is ; n=75 and the consecutive integeres are 12, 13 & 14) Interesting application. Can you elaborate the highlighted Concept ? Thanks the BIG IDEA here: The difference between squares of two consecutive integers = Sum of the two consecutive integers eg: \(10^2  9^2 = (10+9)(109) = 19\) so on and so forth In Statement 1 we are told that (69+n) & (94+n) are the squares of two consecutive integers, So use the above idea: \((94+n)(69+n) = 25\) Since we know that the sum of the two consecutive integers is 25 & to find the individual consecutive integers: 25 = 2n+1 (since integers are consecutive) n = 12 & (n+1) = 13 Now that we have each individual integer: \(12^2 = (69+n)\) \(144 = 69 + n\) \(n = 75\) Same applies for statement 2 Bunuel what does it mean when we write number in this way 25 = 2n+1 Does it mean a consecutive number ? but consecutive numbers are written in this form x, x+1, x+2, x+3, x+4 no ?



Manager
Joined: 11 Sep 2013
Posts: 158
Concentration: Finance, Finance

Re: If the positive integer n is added to each of the integers 69, 94, and
[#permalink]
Show Tags
02 Sep 2018, 08:56
My Approach:
I don't think we have to do any calculation to find the actual value of n.
Because there will be a fixed difference between two square numbers. And if we add any particular number(n) to two numbers we will get that difference. There is no way to get two different values for n. If we try to get two different values for n, it will be impossible to find another answer for two consecutive square numbers.




Re: If the positive integer n is added to each of the integers 69, 94, and &nbs
[#permalink]
02 Sep 2018, 08:56






