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The positive integers p, q, and r each have the same remainder when

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The positive integers p, q, and r each have the same remainder when [#permalink] New post   20 Mar 2023, 09:14
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The positive integers p, q, and r each have the same remainder when divided by 7. What is the value of q?

(1) p - r =q

(2) 30≤ q≤ 40
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The positive integers p, q, and r each have the same remainder when [#permalink] New post   20 Mar 2023, 11:36
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Re: The positive integers p, q, and r each have the same remainder when [#permalink] New post   20 Mar 2023, 23:47
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TBT wrote:
The positive integers p, q, and r each have the same remainder when divided by 7. What is the value of q?

(1) p - r =q

(2) 30≤ q≤ 40


Let
\(p = 7x_1 + z\)
\(q = 7x_2 + z\)
\(z = 7x_3 + z\)

Statement 1

(1) p - r =q

7(x_1 - x_3) = 7x_2 + z

z = 7(x_1 - x_3- x_2)

Therefore z = 0.

We don't know the value of q.

Statement 2

(2) 30≤ q≤ 40

Not sufficient, as there can be multiple values of q.

Combined

From statement 1, we know that q is a multiple of 7, and from statement 2, we know that p lies between 30 and 40. Hence q = 35

Sufficient.

Option C
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Re: The positive integers p, q, and r each have the same remainder when [#permalink] New post   12 Apr 2024, 05:37
gmatophobia wrote:
TBT wrote:
The positive integers p, q, and r each have the same remainder when divided by 7. What is the value of q?

(1) p - r =q

(2) 30≤ q≤ 40

Let
\(p = 7x_1 + z\)
\(q = 7x_2 + z\)
\(z = 7x_3 + z\)

Statement 1

(1) p - r =q

7(x_1 - x_3) = 7x_2 + z

z = 7(x_1 - x_3- x_2)

Therefore z = 0.

We don't know the value of q.

Statement 2

(2) 30≤ q≤ 40

Not sufficient, as there can be multiple values of q.

Combined

From statement 1, we know that q is a multiple of 7, and from statement 2, we know that p lies between 30 and 40. Hence q = 35

Sufficient.

Option C

­How did you deduce from statement 1 that z=0 and that q is a multiple of 7?
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Re: The positive integers p, q, and r each have the same remainder when [#permalink]
12 Apr 2024, 05:37
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