Is 4t^3-2t^2-8t+16 divisible by t^2 ?

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lenagmat: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Oct 16, 2011 2:21 pmFollowed by: 1 member

by lenagmat » Thu Oct 27, 2011 9:03 am

Is 4t^3-2t^2-8t+16 divisible by t^2 ?

1. t>1
2. t is an even prime number

A is B.

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Source: Beat The GMAT — Data Sufficiency | Thu Oct 27, 2011 9:03 am

GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Thu Oct 27, 2011 9:23 am

If 4t^3-2t^2-8t+16 is divisible by t^2, then 4t^3-2t^2-8t+16 divided by t^2 must be an integer.

Start by dividing the expression by t^2. You can do this term by term to get:

4t-2-8/t+16/t^2. We need this to be an integer if the answer is yes, which essentially means t must be something that divides 8, and t^2 must be something that divides 16.

1. This is not helpful. It could be divisible if t=2 or 4. Or not divisible if t=anything else. INSUFFICIENT.

2. this tells us that t=2 because 2 is the only even prime number. As discussed above, this means the expression is, in fact, divisible by t^2. SUFFICIENT.

Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial

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vaibhavgupta: Master | Next Rank: 500 Posts; Posts: 416; Joined: Tue Aug 30, 2011 2:18 pmFollowed by: 9 members; Location: Delhi, India; Thanked: 13 times

by vaibhavgupta » Sat Oct 29, 2011 3:48 pm

lenagmat wrote:Is 4t^3-2t^2-8t+16 divisible by t^2 ?

1. t>1
2. t is an even prime number

A is B.

The only positive Prime number is 2

HenceB

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