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# M22-10

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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16 Sep 2014, 00:16
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Difficulty:

25% (medium)

Question Stats:

73% (00:54) correct 27% (01:18) wrong based on 134 sessions

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$$@$$ represents the tens digit in integer $$A = 1543@2$$. What is the value of $$@$$ ?

(1) $$A$$ is divisible by 9

(2) $$A$$ is divisible by 4

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Joined: 02 Sep 2009
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16 Sep 2014, 00:16
Official Solution:

(1) $$A$$ is divisible by 9. In order an integer to be divisible by 9, the sum of its digit must be divisible by 9. Hence $$1+5+4+3+@+2=15+@$$ must be divisible by 9, and since $$@$$ is a digit then it can only equal to 3. Sufficient.

(2) $$A$$ is divisible by 4. In order an integer to be divisible by 4, its last two digits must be divisible by 4. Hence $$@2$$ must be divisible by 4, which is possible if $$@=1$$, $$@=3$$, $$@=5$$, $$@=7$$, or $$@=9$$. Not sufficient.

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05 Jan 2018, 06:18
+1 for A. A number is divisible by 9 if sum of individual digits is divisible by 9. The sum of digits in this case is 15+@.

Statement 1 : The max sum possible is 24. From 15 to 25, only 18 is divisible by 9. Hence we get a unique value for @.
Statement 2 : The number is divisible by 4 if @2 is divisible by 4. @ could be 1,3, or 5. Ie no unique value !!!

Hence the answer is option A.
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Re: M22-10 &nbs [#permalink] 05 Jan 2018, 06:18
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# M22-10

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