GMAT question - Is the integer n a multiple of 21? - Review
Type: Data Sufficiency
Difficulty: 
Is the integer n a multiple of 21?
- n is a multiple of 14.
- n - 12 is a multiple of 3.
- 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
Explanation
Lets look at this step by step.
Simplify
Can we simplify the question?
The question asks, "Is n a multiple of 21" and it is probably worth noting at this point that this is the same as asking whether n is divisible by both 3 and 7.
Is statement (1) sufficient?
Statement (1) tells us that, "n is a multiple of 14", which means that n is divisible by both 2 and 7.
This is not sufficient to answer the question.
Is statement (2) sufficient?
Statement (2) tells us that, "n - 12 is a multiple of 3", and since 12 is multiple of 3 we can simplify this to n is a multiple of 3, or to put it another way n is divisible by 3.
Again, this is not sufficient to answer the question.
Select an answer
Since neither statement on its own is sufficient to answer the question we know that the answer must be C (Together) or E (Neither).
Statement (1) tells us that n is divisible by 7 and statement (2) tells us that n is divisible by 3.
Therefore both statements together tell us that n is a multiple of 21 and C is the correct answer.
Sorry to differ on this, but I dont think option C is the correct answer. If we consider the case of odd multiples of 21 (21x1, 21x3 ....) then everytime we fail for the 1st condition. However, the second condition satisfies the case to check divisibility with 21. So the answer should be E.
Avisek, C is definitely the correct answer for this question.
If statement 1 and statement 2 are true, then we know that integer n is definitely divisible by 21. Therefore the answer cannot be E because E states that even if you know both statements to be true you cannot decide whether integer n is divisible by 21.
It can take a little while to get your head around exactly how data sufficiency questions work, it would be well worth reviewing our data sufficiency tutorial before continuing with more practice questions.
in statement 2,if we put 28 (14 * 2 from statement 1)as the value of "n" then 28-12=16.which is not the multiple of 3(as defined by statement 2).thus,I guess E should be the right answer
I am still not convinced that C is the correct answer. For Example:
1. 14 - 7 *2 which is straight forward
2. n-12 is a multiple of 3, if you take n to be 18, then 18-12 is a multiple of 3 AND a multiple of 2. Which still does not give us an unambiguous answer if n is a multiple of 21. I think the answer should be E. IMO.
If statement 1 is true then n is divisible by 7, if statement 2 is true then n is divisible by 3. If both are true then n must be divisible by 21 (i.e. a multiple of 21).
If you are not sure about this try find a value for n that is not a multiple of 21 for which both statements are true.
I also think E is the answer. I dont know why C is the answer, maybe the question is not worded properly.
Lets look at this another way.
Values of n that satisfy statement 1 are
..., -14, 0, 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Values of n that satisfy statement 2 are
...-3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 29, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, ...
Therefore values of n that satisfy statements 1 and 2 are
... 0, 42, 84, 126, ...
Which are all multiples of 21 and therefore if statements 1 and 2 are true then n is a multiple of 21 and C is the correct answer.
thank you ... teacher
E is the right answer. Since 14*4 = 42 that is divisible by 3 and 42-12 = 30 that is also divisible by 3 but 30 is not divisible by 21.
eemansaleem, you need to check your math, 14 x 4 = 56 (not 42)
Yes sorry. But i guess the answer was "E" instead of "C"
Joel, I admire your patience.
so do i !
I think its E, and 14*3 = 42, not 14 * 4, which is 56
Sorry, it shouldn't be E
Ans is "c"..
it all makes sense..
What is multiple of number? I think the question is worded incorrectly there.