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# Which of the following integers is the square of an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 52385
Which of the following integers is the square of an integer?  [#permalink]

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12 Jun 2015, 02:12
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Difficulty:

5% (low)

Question Stats:

82% (00:54) correct 18% (01:18) wrong based on 143 sessions

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Which of the following integers is the square of an integer?

(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793

Kudos for a correct solution.

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Re: Which of the following integers is the square of an integer?  [#permalink]

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12 Jun 2015, 03:03
Bunuel wrote:
Which of the following integers is the square of an integer?

(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793

Kudos for a correct solution.

CONCEPT: The unit digit of any Perfect Square can't be 2 or 3 or 7 or 8

Hence Option B, C D and E can be ruled out

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Joined: 02 Aug 2009
Posts: 7211
Which of the following integers is the square of an integer?  [#permalink]

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12 Jun 2015, 03:47
Bunuel wrote:
Which of the following integers is the square of an integer?

(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793

Kudos for a correct solution.

although the numbers look huge, there can be various ways to check whether the number is square integer or not..
here the very first way of sorting out the integers gives us the result..
we check the integer for div by 3 and 9..
if the sum of digits is div by 3 and not 9, that means the number is not square ..

and by a multiple of 9 would mean that it is div by 9 and can be a square..
only A is left, rest all are div by 3 and not by 9...
ans A
had some number been not div by 3, we would have checked these number further...

also units digit of perfect square cannot be 2,3,7 or 8... again only A left
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Which of the following integers is the square of an integer?  [#permalink]

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12 Jun 2015, 04:48
1
Which of the following integers is the square of an integer?

(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793

Solution - Square the each number from 1 to 9 and check the units digit for match. Only 2^2 and 8^2 result to unit digit 4. Hence answer A.

Thanks,

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Joined: 21 May 2013
Posts: 659
Re: Which of the following integers is the square of an integer?  [#permalink]

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13 Jun 2015, 11:45
Bunuel wrote:
Which of the following integers is the square of an integer?

(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793

Kudos for a correct solution.

Simply check the square of each integer from 1 to 100
1=1
2=4
3=9
4=16
5=25
6=36
7=49
8=64
9=81
10=100

Therefore, unit's digit can't be 8,2,7 or3
Manager
Joined: 01 Jan 2015
Posts: 56
Re: Which of the following integers is the square of an integer?  [#permalink]

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14 Jun 2015, 08:57
Perfect Square only ends with 0,1,4,5,6,9
Math Expert
Joined: 02 Sep 2009
Posts: 52385
Re: Which of the following integers is the square of an integer?  [#permalink]

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15 Jun 2015, 03:42
1
Bunuel wrote:
Which of the following integers is the square of an integer?

(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

One way to approach this problem is to factor all of the answer choices. The one with matching pairs of prime factors is a perfect square. Although valid, this approach would be very time-consuming.

There is a backdoor solution: examine the units digit of the answers. Since the units digit of x^2 is simply the units digit of the square of the units digit of x, a perfect square must have the same units digit as one of 0, 1, 4, 9, 16, 25, 36, 49, 64, or 81. That is, a perfect square must have a units digit of 0, 1, 4, 5, 6, or 9. A perfect square cannot have a units digit of 2, 3, 7, or 8. Thus, answer choices B, C, D, and E are disqualified.

By the way, 73,410,624 is (8,568)^2. You would never be expected to figure that out on the GMAT.

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Re: Which of the following integers is the square of an integer?  [#permalink]

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23 Apr 2018, 15:55
Bunuel wrote:
Which of the following integers is the square of an integer?

(A) 73,410,624
(B) 63,398,748
(C) 54,113,892
(D) 42,785,337
(E) 31,298,793

Let’s determine the possible units digits of all perfect squares:

0^2 = 0

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 6

5^2 = 5

6^2 = 6

7^2 = 9

8^2 = 4

9^2 = 1

So perfect squares can have units digits of 0, 1, 4, 5, 6, and 9. Thus, the only possible perfect square is choice A.

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Re: Which of the following integers is the square of an integer? &nbs [#permalink] 23 Apr 2018, 15:55
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# Which of the following integers is the square of an integer?

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