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

My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?

My answer is A, (i am not clear about statemnet 2)

my reason is since 60 is a multiple of 12, so all multiples of 60 will be divisible by 12 because all those multiples will have 60 in them. suppose x=180, then it can also be written as 60*3/12 you can also do and trial and error method to arrive at the answer.

Question in this case, we can't upfront assume that x is an integer. Now when someone says x is a multiple of 60, we mean x=60k. But does k have to be an integer? In other words, can k be fractional with the result that x is a fraction [this thought just occurred to me]. I think multiples mean integer multiples by definition? Of course if you allowed k to be fractional, then A cannot guarantee.
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Question in this case, we can't upfront assume that x is an integer. Now when someone says x is a multiple of 60, we mean x=60k. But does k have to be an integer? In other words, can k be fractional with the result that x is a fraction [this thought just occurred to me]. I think multiples mean integer multiples by definition? Of course if you allowed k to be fractional, then A cannot guarantee.

Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

On GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that: 1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\).

So the terms "divisible", "multiple", "factor" ("divisor") are used only about integers (at least on GMAT).

So "\(x\) is a multiple of 60" means that \(x\) is an integer (\(x=60k\), where \(k\) is an integer)

Its mentioned above that in GMAT unless stated otherwise any given x is assumed to be an integer. Is this assumption correct ?? because this is not the case in CAT or any other mba exam that i have given in the past.
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Its mentioned above that in GMAT unless stated otherwise any given x is assumed to be an integer. Is this assumption correct ?? because this is not the case in CAT or any other mba exam that i have given in the past.

In GMAT, unless mentioned explicitly, a variable "x" should be considered a Real Number(Rational, Irrational Number).

Imaginary or complex numbers are out of GMAT's domain.
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My question is - how do you know that if it's a multiple of 12, then it's ALWAYS multiple of 60?

According to me the answer should be C.

statement 1: 60 * 0 = 0; In other words, 0 is also a multiple of 60; if x=0, then x/12 is not an integer. if x is a multiple of 60 other than 0 then result is an integer. Hence uncertain.

statement 2 : tells us that x is not equal to zero and x is not negative. No clue to answer.

statement 1 & 2 - x is a multiple of 60, and not equal to 0. Implies x is divisible by 12. and the result is an integer. Hence certain, hence "C".

If \(x\) is an integer is \(\frac{x}{12}\) an integer?

(1) \(x\) is a multiple of both 4 and 6 --> \(x\) is a multiple of the least common multiple of 4 and 6, so a multiple of 12, hence \(\frac{x}{12}\) IS an integer. Sufficient.

(2) \(x\) is a multiple of both 8 and 10 --> \(x\) is a multiple of the least common multiple of 8 and 10, so a multiple of 40. Now, if \(x=40\) then the answer is NO but if \(x=120\) then the answer is YES. Not sufficient.

Answer: A.

madzy wrote:

petrifiedbutstanding wrote:

A is the answer.

For stmt 2, x*x*x > 0 could be a mixed fraction. Therefore, insufficient.

when x=0, it is a multiple of 60. but x/12 is not an integer. A cannot be the answer. We need statement 2 as well. 1 & 2 together - C is the answer.

If x=0 then x/12=0=integer (remember: zero is an even integer).
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First statement is pretty straightforward. Second Statement is too easy to dismiss. Normally, the GMAT makes one of the statements a bit more challenging, even on 600-level questions. Nevertheless, not too bad as a practice question for likely-harder GMAT questions.