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In the problem below, AB, CD, and EF are two-digit numbers,

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In the problem below, AB, CD, and EF are two-digit numbers,  [#permalink]

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New post Updated on: 24 Dec 2013, 02:07
5
7
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (02:13) correct 49% (02:27) wrong based on 119 sessions

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In the problem below, AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

Is F prime?

A B
+ C D
______
E F

(1) B and D are consecutive integers.
(2) C = 8.

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Originally posted by madhavsrinivas on 23 Dec 2013, 11:26.
Last edited by Bunuel on 24 Dec 2013, 02:07, edited 1 time in total.
Edited the question.
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Re: In the problem below, AB, CD, and EF are two-digit numbers,  [#permalink]

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New post 23 Dec 2013, 12:22
2
2
1) B and D are consecutive integers.

B + D = F, so possible chioces are:
1+2=3
2+3=5
3+4=7
4+5=9
5+6=1
6+7=3
7+8=5
8+9=7

1) on its own is insufficient. 9 is not prime.



2) C = 8.

If C = 8, then A must equal 1. Otherwise, E will be greater than 9.
So C = 8 implies A = 1 and E = 9.

Still, this doesn't give enough information about F.
B and D could be 2 and 4, in which case F is 6 and not prime, or B and D could be 1 and 2, in which case F is 3, prime.



1) B and D are consecutive integers and 2) C = 8.

Looking at the possible choices from 1) given the constraint of 2), we can eliminate anything that has 1, 8, or 9. So the remaining possible choicse for B + D = F are:
2+3=5
3+4=7
6+7=3

Note, it can't actually be 6+7, because then there will be a carry over. But either way, 5 and 7 ae both prime.

Thus, answer is C - both statements are sufficient to answer the question.
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Re: In the problem below, AB, CD, and EF are two-digit numbers,  [#permalink]

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New post 22 Mar 2019, 03:15
I spent 4 minutes plus and to be honest, I decided to select C out of pure randomness.

Farful's explanation is clear. The key is to stay focus, is F prime, yes or no. That's it.

I tend to get intimidated by the intersection of number properties and data sufficiency (to me this is logic test at the purest).

To be honest, in an exam situation I would most likely try to push as hard as I can for 2 minutes max, and if all else fail pick C out of pure randomness.
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Re: In the problem below, AB, CD, and EF are two-digit numbers,   [#permalink] 22 Mar 2019, 03:15
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In the problem below, AB, CD, and EF are two-digit numbers,

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