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

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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14 Feb 2016, 10:50
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:42) correct 37% (01:48) wrong based on 123 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

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Intern
Joined: 30 Nov 2015
Posts: 8
Re: How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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14 Feb 2016, 12:04
16
24
32
40
48
56
64
72
80
88

96

C
Manager
Joined: 07 May 2015
Posts: 174
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
Re: How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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15 Feb 2016, 21:23
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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17 Feb 2016, 22:13
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

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

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10 Jan 2018, 11:58
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, 11:58
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