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# If the units digit of a^2 + b^2 is 7, which of the following

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Manager
Joined: 14 May 2005
Posts: 85
Location: San Francisco
Followers: 1

Kudos [?]: 2 [0], given: 0

If the units digit of a^2 + b^2 is 7, which of the following [#permalink]  06 Nov 2006, 00:47
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If the units digit of a^2 + b^2 is 7, which of the following could be the units digit of a + b?

3
4
6
8
9
VP
Joined: 25 Jun 2006
Posts: 1175
Followers: 2

Kudos [?]: 71 [0], given: 0

A for me.

the possible combinations are:
a has 1 or 9 as unit digit.
b has 6 or 4 as unit digit.

so only A is possible when a has 9 and b has 4 as unit digit.
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 98 [0], given: 0

(A) for me.

unitDig(x) -> unitDig(x^2)
0 -> 0
1 -> 1
2 -> 4
3 -> 9
4 -> 6
5 -> 5
6 -> 6
7 -> 9
8 -> 4
9 -> 1

The only combination to obtain 7 is 1 + 6. Thus,
we can search and sum the possible unitDig(x):
o 1+4 = 5
o 1+6 = 7
o 4+9 = 13 : Bingo, the unit is 3
o 6+9 = 15
VP
Joined: 15 Jul 2004
Posts: 1473
Schools: Wharton (R2 - submitted); HBS (R2 - submitted); IIMA (admitted for 1 year PGPX)
Followers: 17

Kudos [?]: 115 [0], given: 13

Getting A as well.

of the possible SQUARE digits we have 1, 4, 5, 6, and 9 out of which only 1 and 6 yield 7.

1 and 6 can in turn be obtained from

1, 9

4 and 6

so possible options are 3 and 5. A is right.
Manager
Joined: 14 May 2005
Posts: 85
Location: San Francisco
Followers: 1

Kudos [?]: 2 [0], given: 0

The OA is A (3).

Thanks the for the responses.
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