It is currently 28 Sep 2020, 02:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:
Senior Manager
Joined: 20 May 2014
Posts: 283
Followers: 24

Kudos [?]: 63 [0], given: 220

If k is an integer, what is the smallest possible value of k [#permalink]  20 Nov 2017, 10:45
00:00

Question Stats:

75% (01:00) correct 25% (01:00) wrong based on 20 sessions
If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?

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

Kudos for correct solution.
[Reveal] Spoiler: OA
VP
Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1312 [1] , given: 251

Re: If k is an integer, what is the smallest possible value of k [#permalink]  01 Dec 2017, 22:27
1
KUDOS
Bunuel wrote:
If k is an integer, what is the smallest possible value of k such that 1040k is the square of an integer?

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

Kudos for correct solution.

Here let 1060 can be written as = $$2^4 X 65^1$$

to make it perfect square k should be equal = 65 i.e $$2^4 X 65^2$$

Hence option E
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 94 [0], given: 99

Re: If k is an integer, what is the smallest possible value of k [#permalink]  10 May 2018, 10:44
I multipled each option to 1040 and took a square root by the calculator and I got the answer in 2.03 min .. E
Manager
Joined: 26 Jan 2018
Posts: 189
GRE 1: Q165 V156
Followers: 1

Kudos [?]: 132 [0], given: 3

Re: If k is an integer, what is the smallest possible value of k [#permalink]  11 May 2018, 04:23
65 as that is what is left post factoring. All the factors should have 2 values atleast
Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 94 [0], given: 99

Re: If k is an integer, what is the smallest possible value of k [#permalink]  14 May 2018, 00:47
One should also remember that the exponents of prime factors are even.

or we can solve the problem by taking the prime factorization of 1040 , when we do so we notice the factors of 13 and 5 are not even rather they are only 1 each..

hence we choose the option he because when we multiply 1040 by 65 13 and 5 factors make the exponents of 1040*65 even

hence option is E is correct.
Director
Joined: 09 Nov 2018
Posts: 505
Followers: 0

Kudos [?]: 56 [0], given: 1

Re: If k is an integer, what is the smallest possible value of k [#permalink]  29 Dec 2018, 17:50
IshanGre wrote:
One should also remember that the exponents of prime factors are even.

Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 176 [0], given: 4

Re: If k is an integer, what is the smallest possible value of k [#permalink]  29 Dec 2018, 19:39
Expert's post
AE wrote:
IshanGre wrote:
One should also remember that the exponents of prime factors are even.

Since we are looking for square, the exponent has to be even..
Similarly if we are looking at a cube, the exponent should be divisible by 3..
.1040k=2*520k=$$2^2*260k=2^2*2*130k=2^4*65=2^4*5*13$$
So 2 has a power of 4, and we require one more of 5 and 13 to make the entire term as square
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

MyGuru Representative
Joined: 09 Apr 2020
Posts: 35
Followers: 0

Kudos [?]: 33 [2] , given: 2

Re: If k is a positive integer, what is the smallest possible va [#permalink]  17 Apr 2020, 20:03
2
KUDOS
Expert's post
workout wrote:
If k is a positive integer, what is the smallest possible value of k such that 1040k is the square of an integer?

A) 2

B) 5

C) 10

D) 15

E) 65

Questions like this can often be solved by figuring out prime factors.

We know that 1040 * k is a perfect square, so find the prime factorization of 1040 first:

104*10
2*52* 5*2
2*2*26*5*2
2*2*2*13*5*2

So the prime factorization of 1040 = $$2^4*5*13$$

For a number to be a perfect square, each of its prime factors need to be paired with a matching prime factor.

$$2^4$$ is 16, a perfect square. Each factor of 2 is paired with another factor of 2. But 5 and 13 don't have matching factors, so we need another 5 * 13 to make a perfect square. That product is k.

k = 5*13 = 65

_________________

Steve Markofsky

Intern
Joined: 24 Jan 2020
Posts: 23
Followers: 0

Kudos [?]: 25 [3] , given: 2

Re: If k is a positive integer, what is the smallest possible va [#permalink]  18 Apr 2020, 05:00
3
KUDOS
Prime factorization of 1040 = $$2^4*5*13$$

Since $$\sqrt{2^4}$$ = 4

Since $$2^4$$ is already a perfect square the other factors not having a perfect square are 5 and 13

Hence the lowest number required to be multiplied to 1040 to make it a square = 5 * 13 = 65

Re: If k is a positive integer, what is the smallest possible va   [#permalink] 18 Apr 2020, 05:00
Display posts from previous: Sort by