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
Is the tens digit of a two digit integer k divisible by 3?
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Rephrased question: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
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.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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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.
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.