If k is an integer, what is the smallest possible value of k such that

Question

If k is an integer, what is the smallest possible value of k such that 1040*k is the square of an integer?

A. 2
B. 5
C. 10
D. 15
E. 65

AmoyV · Answer

1040=2^4*13*5

We need 13*5 to be multiplied with 1040 to make is a perfect square.

Therefore, k=13*5=65

Answer : E

OptimusPrepJanielle · Answer

1040 = (2^4)*(13)*(5) We need one more factor of 13 as well as 5 so as to make square of an integer. So, k = 13*5 = 65 Hence option (E). -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

Lucky2783 · Answer

1040K = 13*8*10*K = 13*2^4*5*K
so K should have one 13 and one 5 i.e. 65 Answer E

GSBae · Answer

We need to find a number k such that 1040k = n^2 for some number n.

The prime factorization of 1040 is  2^4 5^1 13^1 .

In order for 1040k to be a square number, we need every prime factor in 1040k to be  at least raised to the second power.   The only numbers that are not are 5 and 13 - thus, we need one more factor of 5 and one more factor of 13. Therefore, k = 5*13 = 65.

Answer: E

PareshGmat · Answer

Answer = E. 65

We require to find factors of 1040 which are perfect squares

1040 = 4 * 4 * 65

To make 1040 a perfect square, it has to be multiplied by 65

k = 65

countonhearts · Answer

1040k - k needs to be replaced.

__1_02________
 1 |1040K
 1
 -------------
 202 | *040k
 404 
K should be 4
102^2 = 10404

SherLocked2018 · Answer

Factorizing 1040 = (2^4).5.13 
Thus we need 5 and 13 to make it a perfect sqaure. 
Thus 65. Ans E.

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: Making_A_Square.png

rhine29388 · Answer

Factorize 1040
1040 = 2 * 2 * 2 * 2 * 5 * 13
as we know that square of any number should have even powers of factors, the only number missing is 5 * 13 = 65
Correct answer - E

jmartin4383 · Answer

1040
 ^
10*104
 ^ ^
 2 * 5  52* 2 
 ^
 26* 2 
 ^
  13 * 2 
2*2*2*2*5*13=1040
2*2*2*2*5*13*K=1040k
(2*2*5*13)=(2*2*K) Since its a square, distribute the 2's and set the sides equal
5*13 = K (Cancel out the 2's)
65=K

nigina93 · Answer

Answer E and here is why, 
First we need to factorize 1040, or 2^4*5*13*k=a perfect square. To have a perfect square, we must have squared variables before equal sign or 5 and 13. So 5*13 is 65

GmatPrime · Answer

Since you need the 'square', so start by taking the square root (which will be equal to the integer we want to find since int*int=1040k)

Now,
(1040k)^1/2

= (2^4 * 13 * 5k)^1/2

= 4 (13 * 5k)^1/2

To make this value an integer,
you need to multiply it with a 13 and a 5 inside the root

therefore, k= 13* 5 = 65

chrtpmdr · Answer

"as we know that square of any number should have even powers of factors"

Can someone give me a link where this rule is discussed in more detail?

(if there even is such a thing)

For example what would I need to do if the number was "1080k"

Prime factorization would be: 3^3 * 2^3 * 5

So I have to add one 3, one 2 and one 5 that all factors are even? Is my thought approach right?

Thank you very much for any input

TheNightKing · Answer

1040=2*2*2*2*5*13
So we need 5 and 13 to make it a perfect square. Which is 65

Kinshook · Answer

Asked: If k is an integer, what is the smallest possible value of k such that 1040*k is the square of an integer?
 
1040 = 2^4*5*13
Smallest integer value of k = 5*13 = 65
1040*65 = 2^4*5^2*13^2 =( 2^2*5*13)^2

IMO E

Chanchal2809 · Answer

How this factor came out??

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If k is an integer, what is the smallest possible value of k such that

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If k is an integer, what is the smallest possible value of k such that

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards