If a is a positive integer, then which of the following must be true

Question

If a is a positive integer, then which of the following must be true of (a − 1)(a)(a + 1)?

I. It is always divisible by 3.
II. It is always divisible by 4.
III. It is non-prime.

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Archit3110 · Answer

we can test the given relation (a − 1)(a)(a + 1) for values of a=1,2,3,4 so on
and see that only option 1 & 3 is valid always
IMO D

LeoN88 · Answer

IMO D.
I. three consecutive numbers always div. by 3
II. check a=2, not possible.
III. The number will have at least one power of 2 and 3 each, so non prime.

LeoN88 · Answer

Archit, (a − 1)(a)(a + 1) is always 3k, shouldn't be a composite number?

Archit3110 · Answer

yes, i did an error solving...

CareerGeek · Answer

In the product of 3 consecutive integers, there will ALWAYS be a multiple of 2 (as multiple of 2 repeats after every 2 integers; 0, 2, 4, . . . ) and a multiple of 3 ALWAYS (as multiple of 3 repeats after every 3 integers; 0, 3, 6, 9, . . . . )

So, if (a − 1)(a)(a + 1) is divisible by 2 and 3; its always divisible by 6

I -  YES 
II -  NO  ( 1*2*3 , 2*3*4, 3*4*5, 4*5*6,  5*6*7 , . . . . )
III -  YES . It will be non-prime as (a − 1)(a)(a + 1) has more than 2 factors always.

IMO Option D

jfranciscocuencag · Answer

What would happen if a=1 (+ve integer)

Then the wole term would be 0.

Thank you  LeoN88 !!!

LeoN88 · Answer

"which of the following must be true"
In these types of sums try to negate options that becomes false under particular situations/conditions.

Zero is divisible by 3. Infact zero is divisible by any number.  jfranciscocuencag

Sanket05 · Answer

In case a = 1 then the product is 0. It is not divisible by 3. Please help

LeoN88 · Answer

Zero is divisible by 3, please get your basic right.

You have zero chocolate, you have to divide it among three children. How much will each get. Answer=0.

If a is a positive integer, then which of the following must be true

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GMAT Problem Solving (PS) Questions

If a is a positive integer, then which of the following must be true

Prep Toolkit

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