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# If r and t are each positive integers less than 10, how many differen

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Re: If r and t are each positive integers less than 10, how many differen [#permalink]
rajtare wrote:
Afroditee wrote:
If r and t are each positive integers less than 10, how many different ordered pairs (r, t) exist such that 7r+7t is a square of an integer?

A. 4

B. 5

C. 6

D. 7

E. 8

7r+7t can be re-written as 7(r+t), now this will be a perfect square if r+t=7, since r,t are positive integers, and less than 10, the possible value of r,t are
(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)

hence correct answer should be C

Why don't we include (0,7) and (7,0) is zero not also an integer? Thanks.

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Re: If r and t are each positive integers less than 10, how many differen [#permalink]
1
Kudos
7 * (r + s) = square of integer

7 * 7 = square

r + s must equal 7.

(1,6)
(2,5)
(3,4)

And the reverse pairs => 6 total
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If r and t are each positive integers less than 10, how many differen [#permalink]
WANGARI8 wrote:
rajtare wrote:
Afroditee wrote:
If r and t are each positive integers less than 10, how many different ordered pairs (r, t) exist such that 7r+7t is a square of an integer?

A. 4

B. 5

C. 6

D. 7

E. 8

7r+7t can be re-written as 7(r+t), now this will be a perfect square if r+t=7, since r,t are positive integers, and less than 10, the possible value of r,t are
(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)

hence correct answer should be C

Why don't we include (0,7) and (7,0) is zero not also an integer? Thanks.

Posted from my mobile device

In GMAT , 0 is not to be considered as either positive or negative
If r and t are each positive integers less than 10, how many differen [#permalink]
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