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

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KSBGC
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X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] 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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Bunuel
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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] New post   24 Jun 2020, 11:17
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Chethan92 wrote:
Bunuel san, Can you edit the answer? It should be A.


Actually the answer is none of the above. It's not mentioned that x is an integer, so if say \(x=\sqrt{68}\), then none of the options give an integer. Not a good question.

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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] 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] 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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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] New post   23 Jun 2020, 08:32
If x =-2/2, it wont be divisible by 6. Why is the answer not A)?
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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] New post   23 Jun 2020, 09:10
The best way is to pick 36 for x^2 and try each of them
But also x^2=32k+4 or 4(8k+1)
X = 2* root of 8k+1
X/2 will leave us with root 8k+1, a possible integer. I.e where k is 1 the integer is 3
X/6 will leave us with root 8k+1 /3, a possible integer since it is odd.i.e when k is 1 X/6 is 1

X/4 will leave us with (root 8k+1)/2 it will always be a fraction

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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] New post   24 Jun 2020, 10:42
What if x=10. Here we will get (10)^2+3=103
103 divided by 32 also leaves a reminder 7.

However, 10/6 is not an integer.

So only Option A is correct, in my opinion.
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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] New post   24 Jun 2020, 11:02
Bunuel san, Can you edit the answer? It should be A.
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Re: X^2+3 is divided by 32 leaves a reminder 7. Which of the following is [#permalink] New post   24 Jun 2020, 11:28
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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


Here is a proper question: if-x-is-a-positive-integer-and-x-2-3-divided-by-32-leaves-a-reminder-327499.html

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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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