Is x a multiple of 9? (1) x = (b!)(c), where b and c are distinct int

Question

Is x a multiple of 9?

(1) x = (b!)(c), where b and c are distinct integers greater than 2.
(2) x is a multiple of integer c and c < 4

CareerGeek · Answer

(1) x = (b!)(c), where b and c are distinct integers greater than 2. —> Nothing can be said about the values of b & c —> Insufficient (2) x is a multiple of integer c and c < 4 —> x can be a multiple of 2 or 3 or 2^2 or 3^2 so on ... —> Insufficient Combining (1) & (2), b & c are distinct integers greater than 2 and c < 4 —> c = 3 only Also, b can take values 4 or above —> b! Will always have a 3 multiple —> b! = 3p, for any positive integer p —> x = b!c = 3p*3 = 9p —> x is always a multiple of 9 IMO Option C Posted from my mobile device

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) If b = 3 and c =3, then x=(3!)*3 = 18 which is a multiple of 9 and the answer is 'yes'. If b = 3 and c =4, then x=(3!)*4 = 24 which is not a multiple of 9 and the answer is 'no'. Since condition 1) does not yield a unique answer, it is not sufficient. Condition 2) If c = 3 and x = 18, then x is a multiple of 9 and the answer is 'yes'. If c = 3 and x = 12, then x is not a multiple of 9 and the answer is 'no'. Since condition 2) does not yield a unique answer, it is not sufficient. Conditions 1) & 2) Since c is an integer with 2 2 and b≠3=c we have b≥4 and b! is always a multiple of 3. Thus, x = (b!)c is a multiple of 9 and the answer is 'yes', since both b! and c are multiples of 3. Since both conditions together yield a unique answer, they are sufficient. Therefore, C is the answer. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

merajul · Answer

Is x a multiple of 9?

(1) x = (b!)(c), where b and c are distinct integers greater than 2.
(2) x is a multiple of integer c and c < 4[/quote]

From (1) we get, b >2 & c>2 . We are not sure about the exact value of the both. (INSUFFICENT)

From (2) we get, c<4, so c = 1,2 or 3 . Further we don't the value of b. (INSUFFICIENT)

(1) + (2) we get, 2<c<4 . Thus c must be 3.

Now, since b>2, we can take any value greater than 2, like 3,4,5,6 ... and so on.

x = (b!) (c)

x = (3!) (3) = (3*2*1) (3) , divisible by 9 or multiple of 9
x = (4!) (3) =(4*3*2*1) (3) , 3*3=9 multiple
x = (5!) (3) = (5*4*3*2*1) (3) , 3*3=9 multiple
.
.
. and so one.

Thus combining both should be SUFFICIENT. Option C is the right answer.

Is x a multiple of 9? (1) x = (b!)(c), where b and c are distinct int

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GMAT Data Sufficiency (DS) Questions

Is x a multiple of 9? (1) x = (b!)(c), where b and c are distinct int

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