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sequence for A and B

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sequence for A and B

by jsk988 » Sun Jul 26, 2009 1:01 am
Here is the below problem:
Sequence A is defined by the equation An = 3n + 7, where n is an integer greater than or equal to 1. If set B is comprised of the first x terms of sequence A, what is the median of set B ?

(1) The sum of the terms in set B is 275.

(2) The range of the terms in set B is 30.

I know the answer which is either is sufficient. My question is.. what happens if the sum is incorrect? i.e. if there isn't an integer n that allows the values to add up to the sum... will it be considered insufficient?
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Re: sequence for A and B

by Ian Stewart » Sun Jul 26, 2009 6:44 am
jsk988 wrote: My question is.. what happens if the sum is incorrect? i.e. if there isn't an integer n that allows the values to add up to the sum... will it be considered insufficient?
In real GMAT questions, the information in a DS question is always 'logically consistent'. That is, it's *always* possible for all of the information given in the question and in the statements to be simultaneously true. So the situation you're asking about could never happen on the real test. If a statement says "The sum of the elements of set S is 275", there absolutely must be at least one way this could happen. Very often in DS your task is to determine whether there is only one way it could happen, or more than one way, but there's always at least one.

That said, I've seen many questions designed by test prep companies that violate this rule, so you may run across a few questions (not official questions, though) which contain inconsistent information. Logically speaking, if information is inconsistent in a DS question, there is no way to decide on a correct answer. For example, a question like the following would be nonsensical:

What is the value of x?
1) x is negative
2) x > 1

It's not possible to decide on a correct answer here. Clearly using both statements, there is no possible value of x. Many people would thus consider the two statements together sufficient; we know with certainty there is no value of x possible. Many others would consider the two statements together insufficient, since you can't find x even using all your information. Both positions are perfectly defensible, so a question like this doesn't make any sense as a DS question, since it has two different legitimate right answers. Because of this, all real GMAT DS questions must always contain consistent information.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by bhumika.k.shah » Mon Mar 01, 2010 4:03 am
How to solve this problem ?
i figured that the #s are evenly arranged with a gap of 3

But then what ?

i dint know how to solve any further and hence randomly guessed C

Which is obviously wrong.

:(
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by bhumika.k.shah » Mon Mar 01, 2010 4:10 am
How is statement B sufficient.

i know A is - for sure
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by Fiver » Tue Mar 02, 2010 7:25 am
bhumika.k.shah wrote:How is statement B sufficient.

i know A is - for sure
The nos. in the series are 10, 13, 16, 19, 22...
and set B contains 'x' of these terms; we are asked for the median of set B.

(1) The sum of the terms in set B is 275.
275 = x/2(20 + 3(x-1))
Suff as we could solve for x and find the median term

(2) The range of the terms in set B is 30.
30 = LT - FT
30 = LT - 10
hence LT = 40
and 40 = 10 + 3(x-1)
x = 11 and the median will be the 6th term, which is 3*6 + 7 = 25

Hence D
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by ShakeM » Tue Mar 02, 2010 9:54 am
Can someone explain it again, I can't seem to understand.....
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by madsadman » Fri Mar 05, 2010 12:49 am
I will try to explain it...
B will contain all numbers from 3*1+7 to 3*x+7
Sum of all numbers = 3*1 + 7 + 3*2 + 7 + 3*3+7 + ..... 3* x + 7 which is equal to (3x/2)(x+1) + 7x. Let it be Y
Range of numbers = 3*x + 7 - (3*1 + 7) which is equal to 3(x - 1). Let it be Z.

From (i) we have
Y = 275. The equation can be easily solved hence (i) is sufficient.

From (ii) we have
Z = 30. This can be solved to give the value of x.

So the answer is 'D'.
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