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can somone explain

by grandh01 » Sun Aug 12, 2012 5:32 pm
If a1, a2, a3, . . . , an, . . . is a
sequence such that an=2n for all n
≥ 1, is ai greater than aj ?
(1) i is odd and j is even
(2) i^2 > j^2
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Aug 12, 2012 7:05 pm
grandh01 wrote:If a1, a2, a3, . . . , an, . . . is a
sequence such that an=2n for all n
≥ 1, is ai greater than aj ?
(1) i is odd and j is even
(2) i^2 > j^2
(1) i is odd and j is even.
If i = 3, j = 2, then aj = a2 = 2 * 2 = 4, ai = a3 = 2 * 3 = 6. Here ai > aj.
If i = 1, j = 2, then ai = a1 = 2 * 1 = 2, aj = a2 = 2 * 2 = 4. Here ai < aj.
No definite answer; NOT sufficient.

(2) i² > j²
n ≥ 1 implies i > j (as i² > j²)
ai = 2i and aj = 2j
i > j implies 2i > 2j or ai > aj; SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Mon Aug 13, 2012 6:20 am
grandh01 wrote:If a1, a2, a3, . . . , an, . . . is a
sequence such that an=2n for all n
≥ 1, is ai greater than aj ?
(1) i is odd and j is even
(2) i^2 > j^2
First, let's get an idea of how this sequence looks: {2,4,6,8,10...}

Target question: Is term i > term j?
Since the terms in our sequence increase with each successive term, we can see that term i will be great than term j if term i occurs after term j in the sequence.
So, we can rewrite the target question as: Is i > j?

Statement 1: i is odd and j is even
This doesn't help us answer our rephrased target question.
INSUFFICIENT

Statement 2: i^2 > j^2
Since we're dealing with positive, integer values of i and j, we can conclude that, if i^2 > j^2, then i > j
This is certainly enough information to answer our rephrased target question.
SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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