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Is the tens digit of a two digit integer k divisible by 3?

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Is the tens digit of a two digit integer k divisible by 3?

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Is the tens digit of a two digit integer k divisible by 3?

(1) k-5 is a multiple of 3
(2) k-11 is a multiple of 3

OA E

Source: Manhattan GMAT

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Question = Is the tens digit of a two digit integer K divisible by 3?

Statement 1 :
K - 5 = Multiple of 3
If K = 20
20 - 5 = 15
However, 15 is a multiple of 3 the tens digit of K is 2 which is not divisible by 3.
Hence, statement 1 is NOT SUFFICIENT.

Statement 2 :
K - 11 = Multiple of 3
If K = 53
53 - 11 = 42
However, 42 is a multiple of 3, the tens digit of K here is 5 which is not divisible by 3.
Hence, Statement 2 is NOT SUFFICIENT.

Giving that statement 1 and 2 are the same, combining them together would = NOT SUFFICIENT.
Option E is the correct answer.

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BTGmoderatorDC wrote:
Is the tens digit of a two digit integer k divisible by 3?

(1) k-5 is a multiple of 3
(2) k-11 is a multiple of 3

OA E

Source: Manhattan GMAT
Rephrased question:
is the tens digit of k a 3, 6, or 9?


Test values with the statement to try to prove insufficiency:

(1) k - 5 is a multiple of 3
This tells us that k is 5 more than some multiple of 3. Test some 2-digit multiples of 3:

Case 1: 3x = 27 --> k = 32.
Is the tens digit a multiple of 3? Yes.

Case 1: 3x = 42 --> k = 47.
Is the tens digit a multiple of 3? No.
Insufficient.

(2) k - 11 is a multiple of 3
This tells us that k is 11 more than some multiple of 3. Test some 2-digit multiples of 3:

Case 1: 3x = 27 --> k = 38.
Is the tens digit a multiple of 3? Yes.

Case 1: 3x = 42 --> k = 53.
Is the tens digit a multiple of 3? No.
Insufficient.

(1) & (2) Together
k is a number that is 5 more than some multiple of 3, and also 11 more than a multiple of 3. But since 5 and 11 are 6 apart, any given number that's 5 more than a multiple of 3 will also be 11 more than some other multiple of 3:
38: 5 more than 33, 11 more than 27
53: 5 more than 48, 11 more than 42.

Since we can come up with a value for k in the 30s and one in the 50s that fit both statements, we don't have enough to answer the question.

The answer is E.

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Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


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