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

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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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New post 30 Nov 2019, 06:13
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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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X^2+3 is divided by 32 leaves a reminder 7. Which of the following is  [#permalink]

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New post 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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New post 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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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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