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How many positive two-digit numbers, ab, are possible such that ab is

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Joined: 02 Sep 2009
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How many positive two-digit numbers, ab, are possible such that ab is [#permalink]

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New post 14 Feb 2016, 09:50
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Difficulty:

  55% (hard)

Question Stats:

57% (01:06) correct 43% (01:08) wrong based on 98 sessions

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How many positive two-digit numbers, ab, are possible such that ab is divisible by 8 and the sum of a and b is divisible by 8?

A. 0
B. 1
C. 2
D. 3
E. 4
[Reveal] Spoiler: OA

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Re: How many positive two-digit numbers, ab, are possible such that ab is [#permalink]

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New post 14 Feb 2016, 11:04
16
24
32
40
48
56
64
72
80
88

96

C
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Re: How many positive two-digit numbers, ab, are possible such that ab is [#permalink]

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New post 15 Feb 2016, 20:23
only 80 and 88
Ans:c
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Re: How many positive two-digit numbers, ab, are possible such that ab is [#permalink]

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New post 17 Feb 2016, 21:13
Hi All,

From the answer choices, we know that there cannot be that many 2-digit numbers that fit the given 'restrictions' in the prompt, so we really just have to go about finding them with a bit of brute-force. The answers are 'close together' though, so you should insist on writing everything on the pad so that you don't accidentally miss one of the numbers (and choose one of the wrong answers).

We're asked to find the number of positive two-digit numbers that are divisible by 8 AND the sum of the two digits is divisible by 8.

We can list the numbers one at a time, then note whether the sum of the digits is divisible by 8 or not:

16 no
24 no
32 no
40 no
48 no
56 no
64 no
72 no
80 YES
88 YES
96 no

Final Answer:
[Reveal] Spoiler:
C


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Joined: 02 Apr 2014
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Re: How many positive two-digit numbers, ab, are possible such that ab is [#permalink]

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New post 10 Jan 2018, 10:58
a b digit_sum divisible by 8
2 6 8 NO
4 4 8 NO
6 2 8 NO
8 0 8 YES
8 8 16 YES

{80,88} => (C)
Re: How many positive two-digit numbers, ab, are possible such that ab is   [#permalink] 10 Jan 2018, 10:58
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How many positive two-digit numbers, ab, are possible such that ab is

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