If n and q are positive integers, what is the units digit of q?

Question

(1) q = (n)(n + 1)(n + 2)(n + 3)(n + 4)(n + 5)
(2) (n + 1) + n = 9

Skywalker18 · Answer

(1) q = (n)(n + 1)(n + 2)(n + 3)(n + 4)(n + 5)
q is product of 6 consecutive positive integers 
if n = 1
q= 1*2*3*4*5*6
In any 6 consecutive positive integers , we will have a factors of 5 and 2
Hence , the units digit of q will be 0
Sufficient

(2) (n + 1) + n = 9 
=>2n = 8
=> n = 4
We have no information about integer q
Not sufficient

Answer A

ronny123 · Answer

Statement A :
 q = (n)(n + 1)(n + 2)(n + 3)(n + 4)(n + 5)
q is a product of 6 consecutive positive integers

for example : q = 6 x 7 x 8 x 9 x 10 x 11
 or = 242 x 243 x 244 x 245 x 246 x 247

The trick is to notice each product is a multiple of 5

So, the units digit of q can be 5 or 0
Not Sufficient

Statement B :
(n + 1) + n = 9
2n = 8
n= 4

Not sufficient to give the units digit of q on its own

Combining both statements, we get 
q = 4 x 5 x 6 x 7 x 8 x 9

This gives us 5 as the units digit of q

Correct Option : C

sashaman14 · Answer

Disagree with your first point. The unit will always be zero. Your example has 242*245.... ends in zero. 
You will always have a 2*5...which will end in a zero. 
Answer is A

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If n and q are positive integers, what is the units digit of q?

(1) q = (n)(n + 1)(n + 2)(n + 3)(n + 4)(n + 5)
(2) (n + 1) + n = 9 
 
 In the original condition, there are 2 variables(n,g), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), from n=4, q=(4)(5)(6)(7)(8)(9)=........0, 0 is derived for ones, which is unique and sufficient. So, the answer is C.
However, this is an integer question, one of the key questions, and apply the mistake type 4(A). 
For 1), q is multiplication of 6 consecutive integers, which means it always has 5 and 2. 
So, there is always 0 for ones, which is unique and sufficient.
For 2), although n=4, there is no date about q, which is not sufficient.
So, the answer is A.
When both C and A are likely to be an answer, the actual answer is A.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

Balajikarthick1990 · Answer

Dear ronny

answer is A...

units digit means last digit and it is going to be 0 if their is a (5,2) combo when you split n into prime factors.
Hope u got it.

If n and q are positive integers, what is the units digit of q?

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GMAT Data Sufficiency (DS) Questions

If n and q are positive integers, what is the units digit of q?

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