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# In the x-y coordinate plane, the distance between (p,q) and (1,1) is 5

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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In the x-y coordinate plane, the distance between (p,q) and (1,1) is 5  [#permalink]

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10 Aug 2018, 02:36
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75% (hard)

Question Stats:

45% (01:57) correct 55% (01:56) wrong based on 38 sessions

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[Math Revolution GMAT math practice question]

In the x-y coordinate plane, the distance between $$(p,q)$$ and $$(1,1)$$ is $$5$$. If $$p$$ and $$q$$ are integers, how many possibilities are there for the point $$(p,q)$$?

$$A. 2$$
$$B. 4$$
$$C. 8$$
$$D. 12$$
$$E. 16$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Status: Learning stage Joined: 01 Oct 2017 Posts: 1028 WE: Supply Chain Management (Energy and Utilities) Re: In the x-y coordinate plane, the distance between (p,q) and (1,1) is 5 [#permalink] ### Show Tags 10 Aug 2018, 03:25 MathRevolution wrote: [Math Revolution GMAT math practice question] In the x-y coordinate plane, the distance between $$(p,q)$$ and $$(1,1)$$ is $$5$$. If $$p$$ and $$q$$ are integers, how many possibilities are there for the point $$(p,q)$$? $$A. 2$$ $$B. 4$$ $$C. 8$$ $$D. 12$$ $$E. 16$$ The distance between $$(p,q)$$ and $$(1,1)$$ is $$5$$ Or, $$(p-1)^2+(q-1)^2=5^2$$ 1) $$(p-1)^2+(q-1)^2=5^2+0^2$$; so$$(p-1)^2=0$$ and $$(q-1)^2=5^2$$. Possible pairs of (p,q):-(0,5), (0,-5),(5,0), (-5,0) ----(4 pairs) 2)$$(p-1)^2+(q-1)^2=5^2=4^2+3^2$$;so $$(p-1)^2=4^2$$ and $$(q-1)^2=3^2$$. Possible pairs of (p,q):-(5,4), (5,-2),(-3,4), (-3,-2)---(4 pairs) 3)$$(p-1)^2+(q-1)^2=5^2=3^2+4^2$$;so $$(p-1)^2=3^2 and (q-1)^2=4^2$$. Possible pairs of (p,q):-(4,5), (-2,5),(4,-3), (-2,-3)---(4 pairs) N,B,:- If $$(x-a)^2=k$$ , then $$\sqrt{(x-a)^2}=|x-a|=+k$$ or $$-k$$ Total number of (p,q) pairs=4+4+4=12 Ans. (D) _________________ Regards, PKN Rise above the storm, you will find the sunshine Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7609 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the x-y coordinate plane, the distance between (p,q) and (1,1) is 5 [#permalink] ### Show Tags 13 Aug 2018, 06:29 => (p-1)^2 + (q-1)^2 = 5^2 If p – 1 = ±3, and q - 1 = ±4, then p = 1 ± 3, and q = 1 ± 4. There are four possible points: ( p, q ) = ( 4, 5 ), ( 4, -3 ), ( -2, 5 ), ( -2, -3 ). If p – 1 = ±4, and q - 1 = ±3, then p = 1 ±4, and q = 1 ± 3. There are four possible points: ( p, q ) = ( 5, 4 ), ( 5, -2 ), ( -3, 4 ), ( -3, -2 ). If p – 1 = 0, and q - 1 = ±5, then p = 1, and q = 1 ±5. There are two possible points: ( p, q ) = ( 1, 6 ), ( 1, -4 ). If p – 1 = ±5, and q - 1 = 0, then p – 1 = ±5, and q = 1. There are two possible points: ( p, q ) = ( 6, 1 ), ( -4, 1 ). There are a total of 4 + 4 + 2 + 2 = 12 possibilities for the point (p,q). Therefore, the answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: In the x-y coordinate plane, the distance between (p,q) and (1,1) is 5   [#permalink] 13 Aug 2018, 06:29
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