If k is the quotient when a is divided by b, and a and b are distinct

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

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IanStewart · Answer

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 Statement 1 is true, we're dividing a single-digit prime number a by 2. Since a is different from b, we're dividing an odd prime by 2, so the decimal will end in .5, and Statement 1 is sufficient.

Since k = a/b, Statement 2 tells us that a/b > b, or that a > b^2. If that's true, b clearly cannot be 3 or greater, since that would force a to be greater than 9, and we know a is a single-digit prime. So Statement 2 ensures that b = 2, and is sufficient as well, and the answer is D.

dips1122 · Answer

How can we assume that we need to find the tenth place after the decimal point? Isn't the question wrong? "Tenth place of the quotient when a single-digit prime number is divided by another" will anyway be 0.

IanStewart · Answer

The word 'quotient' has two distinct (though related) definitions in math. It can mean "the result of a division". Under that definition, the quotient when you divide, say, 11 by 4, is 2.75. I have definitely never seen the real GMAT use the word "quotient" with this meaning.

It can also mean "the integer result of a division, ignoring remainders". Then the quotient when you divide 11 by 4 is simply 2 (with a remainder of 3). I may have seen the word used this way in one official GMAT question (at most), but I can't be certain. That's the meaning of 'quotient' I've seen most often in my mathematical life (though I did grad school in Number Theory, so I'd naturally have seen this integer definition more than the other one).

Clearly in this question they intend the first definition above, which is why I find the wording problematic. It's only with that first definition that the question makes any sense, because under the second definition, the answer would necessarily be zero, as you point out.

QuantMadeEasy · Answer

possible distinct values of a and b are {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, the tenths digit is 5. Sufficient

D is correct.

exc4libur · Answer

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.   sufic

b=even=2: a={3,5,7}… a/b={3,5,7}/2…={1.5,2.5,3.5}=tenths(5)

(2) k > b   sufic

k>b: a/b>b, a>b^2, b=2: a={3,5,7}… a/b={3,5,7}/2…={1.5,2.5,3.5}=tenths(5)

Ans (D)

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If k is the quotient when a is divided by b, and a and b are distinct

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If k is the quotient when a is divided by b, and a and b are distinct

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