Question: If k is the quotient when a is divided by b, and a and b are distinct single digit prime numbers, what is the value of the tenths digit of k?

1. b is even
2. k > b

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Approach Solution (1):
The wording is problematic here, because ‘quotient’ often refers to the integer result (ignoring remainders) of a division. That’s not what they mean here; they intend ‘quotient’ to mean the result of the division a/b
If S1 is true, we are dividing a single-digit prime number a by 2. Since a is different from b, we are dividing an odd prime by 2, so the decimal will end in .5, and S1 is sufficient
Since k = a/b, S2 tells us that a/b > b, or that. If that’s true, b clearly cannot be 3 or greater than 9, and we know a is a single-digit prime. So S2 ensures that b = 2, and is sufficient as well

Correct option: D

Approach Solution (2):
Assuming “quotient” is the value of a/b (rather than the integer)
(a, b) = distinct. digit. Primes = {2, 3, 5, 7}
(1) b is even
b = even = 2: a = {3, 5, 7}/ 2 = {1.5, 2.5, 3.5} = tenths (5)
Sufficient
(2) k > b
k > b : a/b > b,, b = 2: a = {3, 5, 7}… a/b = {3, 5, 7}/2 = {1.5, 2,5, 3,5} = tenths (5)

Correct option: D

Approach Solution (3):
Possible distinct values of a and b {2,3,5,7}
(1) b = 2, when 3, 5, 7 are divided by 2, tenths digit is 5
Sufficient
(2) Only when b = 2, quotient is greater than divisor
When dividing 2 or 3 or 5 by 2, then tenths digit is 5
Sufficient

Correct option: D

“If k is the quotient when a is divided by b, and a and b are distinct single digit prime numbers, what is the value of the tenths digit of k?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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