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# X^2+3 is divided by 32 leaves a reminder 7. Which of the following is

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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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X^2+3 is divided by 32 leaves a reminder 7. Which of the following is  [#permalink]

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30 Nov 2019, 06:13
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65% (hard)

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31% (01:29) correct 69% (02:05) wrong based on 26 sessions

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$$X^2$$+3 is divided by 32 leaves a reminder 7. Which of the following is a integer?

I. X/2
II. X/4
III.x/6

A. I
B.II
C. I and II
D. I and III
E. I, II and III
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Joined: 16 Sep 2011
Posts: 107
X^2+3 is divided by 32 leaves a reminder 7. Which of the following is  [#permalink]

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30 Nov 2019, 06:36
KSBGC wrote:
$$X^2$$+3 is divided by 32 leaves a reminder 7. Which of the following is a integer?

I. X/2
II. X/4
III.x/6

A. I
B.II
C. I and II
D. I and III
E. I, II and III

x^2+3 when divided by 32 gives remainder 7
x^2+3= 32k+7
which mean x^2 = 32k +4...so now remainder is 4 for x^2 when divided by 32

lets say k=0, x^2=4 hence x =2 or -2 when divided by 2 will give an integer
but x when divided by 4 will not be integer, so is the case with 6

when k=1 , x^2=36 hence x= 6 or -6 when divided by 2 yields integer
but dividing by 4 does not give integer while with 6 it gives an integer

so combing both only x divided by 2 is common and applicable to most of the cases
As the question asks which one may be integer so all 3 options qualify for same
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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is  [#permalink]

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30 Nov 2019, 11:10
KSBGC wrote:
$$X^2$$+3 is divided by 32 leaves a reminder 7. Which of the following is a integer?

I. X/2
II. X/4
III.x/6

A. I
B.II
C. I and II
D. I and III
E. I, II and III

$$X^2$$+3 is divided by 32 leaves a reminder 7, hence the least possible value of $$X^2$$+3 = 39

So, $$x^2 = 36$$

Or, $$x = +- 6$$

I. $$x/2 = + - 3$$
II. $$x/4 = + - 1.50$$
III. $$x/6 = + - 1$$

Hence, answer must be (D) Only (I) and (III)

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Thanks and Regards

Abhishek....

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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is   [#permalink] 30 Nov 2019, 11:10
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