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If XY, PQ, and RS represent unique two-digit integers, what is the uni

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If XY, PQ, and RS represent unique two-digit integers, what is the uni [#permalink] New post   20 Apr 2016, 00:59
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If XY, PQ, and RS represent unique two-digit integers, what is the units digit of (XY)^2 + (PQ)^2 + (RS)^2?

(1) Y = 1, Q = 2, and S = 3
(2) X = 4, P = 5, and R = 6
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Re: If XY, PQ, and RS represent unique two-digit integers, what is the uni [#permalink] New post   20 Apr 2016, 12:24
We have to find the units digit of (XY)^2 + (PQ)^2 + (RS)^2 --> Units digit of (Y^2 + Q^2 + S^2)

St1: Y = 1; Q = 2; S = 3 --> Units digit of (1 + 4 + 9) = 4. Sufficient

St2: X = 4, P = 5, and R = 6 --> Clearly insufficient as Y, Q and S may take multiple values and units digit differs accordingly.

Answer: A
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Re: If XY, PQ, and RS represent unique two-digit integers, what is the uni [#permalink] New post   20 Apr 2016, 15:34
If XY, PQ, and RS represent unique two-digit integers, what is the units digit of (XY)^2 + (PQ)^2 + (RS)^2?

(1) Y = 1, Q = 2, and S = 3
(2) X = 4, P = 5, and R = 6


To find the units digit of (XY)^2 + (PQ)^2 + (RS)^2, we require the values of Y, Q, S

Statement 1: Sufficient as this gives us information we are looking for.

Statement 2: NS. Only tens digits are given no information about Y,Q or S.

Hence Answer A.
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Re: If XY, PQ, and RS represent unique two-digit integers, what is the uni [#permalink] New post   20 Apr 2016, 22:00
Bunuel wrote:
If XY, PQ, and RS represent unique two-digit integers, what is the units digit of (XY)^2 + (PQ)^2 + (RS)^2?

(1) Y = 1, Q = 2, and S = 3
(2) X = 4, P = 5, and R = 6


Last digit matters generally for unit digit problems...A suffices that.
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Re: If XY, PQ, and RS represent unique two-digit integers, what is the uni [#permalink] New post   21 Apr 2016, 00:12
Only digit numbers are involve hence A is sufficient.
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Re: If XY, PQ, and RS represent unique two-digit integers, what is the uni [#permalink]
21 Apr 2016, 00:12
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