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

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 49251
How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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New post 14 Feb 2016, 10:50
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (01:10) correct 42% (01:09) wrong based on 113 sessions

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Intern
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Joined: 30 Nov 2015
Posts: 9
Re: How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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

96

C
Manager
Manager
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B
Joined: 07 May 2015
Posts: 175
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
GMAT ToolKit User
Re: How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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New post 15 Feb 2016, 21:23
only 80 and 88
Ans:c
EMPOWERgmat Instructor
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Status: GMAT Assassin/Co-Founder
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Joined: 19 Dec 2014
Posts: 12411
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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New post 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

Final Answer:

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Joined: 02 Apr 2014
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GMAT 1: 700 Q50 V34
Re: How many positive two-digit numbers, ab, are possible such that ab is  [#permalink]

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New post 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 &nbs [#permalink] 10 Jan 2018, 11:58
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