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 Post subject: GMAT Algebra
PostPosted: Wed Apr 10, 2013 2:56 am 
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Does 8x = 16 + 2x?
(1) -3x is greater than or equal to -9.
(2) 2x is greater than or equal to 6.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(B) We can simplify 8x = 16 + 2x by subtracting 2x from both sides, resulting in 6x = 16, or x = 8/3. So, the question is essentially asking whether x equals 8/3. If a
statement provides enough information to answer yes or no in a definitive manner, then the statement is sufficient.

Statement (1) tells us that -3x is greater than or equal to -9. After dividing by -3, we get x is less than or equal to 3 (remember to change the direction of the inequality when multiplying or dividing by a negative number). If x can be any number less than or equal to 3, then we do not know for sure whether x equals 8/3. So, Statement (1) is insufficient.

Statement (2) tells us that x is greater than or equal to 3. This means that x could NEVER be less than 3, and therefore could NEVER be equal to 8/3. If we go back to the original statement,Does 8x = 16 + 2x?, we see that the answer is definitely NO (it is never yes).

Remember that your goal in Data Sufficiency questions is to determine whether or not you have enough information to answer the question. The answer does not have to be yes. If the answer is always no, the statement is also sufficient. So, Statement (2) is sufficient because the answer is always no.

Since only Statement (2) is sufficient, the answer must be (B).
----------

By solving this equation we find that if 8x DOES equal 16 plus 2x, then x must equal 8/3, or 2 and 2/3.

statement 1 tells us x is less than or equal to 3
statement 2 tells us x is greater than or equal to 3

Either statement is SUFFICIENT to answer the question. if we take statement 1, then 8x DOES equal 16 + 2x.

However, if we take statement 2, then it does not. Either statement is sufficient to answer the question, though they each yield different answers.


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 Post subject: Re: GMAT Algebra
PostPosted: Wed Apr 10, 2013 2:57 am 
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The statement (1) implies that x ≤ 3.

If x = 8/3 then 8x = 16 + 2x.
If x = 0 then 8x ≠ 16 + 2x.

Therefore the statement (1) is NOT sufficient by itself.


Be careful not to confuse which statement should follow and which one is given.

"If x = 8/3 then x ≤ 3" is TRUE.
"If x ≤ 3 then x = 8/3" is clearly NOT TRUE.

In the question the statement x ≤ 3 is given as the statement (1) and the statement x = 8/3 should be examined.


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 Post subject: Re: GMAT Algebra
PostPosted: Wed Apr 10, 2013 2:57 am 
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That would never happen on the GMAT. Part (i) and Part (ii) never contradict each other. This is misleading.


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 Post subject: Re: GMAT Algebra
PostPosted: Wed Apr 10, 2013 2:59 am 
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There is NO contradiction.
Like in many other data sufficiency questions:
- each statement alone defines a possible range of values;
- the both statements combined result in the intersection of those ranges;
- if all the elements in the intersection answer the statement question identically, then the both statements combined are sufficient.

(1) -3x is greater than or equal to -9
x ≤ 3
Tells us that the possible values of x are:
Image

(2) 2x is greater than or equal to 6
x ≥ 3
Tells us that the possible values of x are:
Image

When we combine the both statements the range of possible values is just one point:
Image
Image

In similar questions this intersection could be some other range, like 1 < x < 2 or -1 < x ≤ 0, etc.
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 Post subject: Re: GMAT Algebra
PostPosted: Wed Apr 10, 2013 3:01 am 
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From 8x = 16 + 2x we have x = 8/3.

From (1) x ≤ 3
From (2) x ≥ 3

then, answer A is correct.


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 Post subject: Re: GMAT Algebra
PostPosted: Wed Apr 10, 2013 3:02 am 
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questioner wrote:
From 8x = 16 + 2x we have x = 8/3.

From (1) x ≤ 3
From (2) x ≥ 3

then, answer A is correct.
Apparently, you confused given information and what the question was asking. Look at these two different statements to feel the difference:
"If x = 8/3 then x ≤ 3" is TRUE.
"If x ≤ 3 then x = 8/3" is NOT TRUE.

In this particular problem the question asks: "Is x = 8/3 ?". The given information is:
1) Statement (1) alone: x ≤ 3
2) Statement (2) alone: x ≥ 3
3) The both statements combined: x = 3

1) If we know that x ≤ 3 then x can be 8/3. But it also can be 3, or any other value less than 3. So we can not give a definite answer to the question. Statement (1) by itself is NOT sufficient.

Question: Does 8x = 16 + 2x IF -3x ≥ -9?
Answer: It can be, but not necessarily.

2) If we know that x ≥ 3 then x definitely cannot be 8/3. So we can give the definite answer to the question. This definite answer is "NO".

Question: Does 8x = 16 + 2x IF 2x ≥ 6?
Answer: NO.


The information in Statement (2) is sufficient to answer the question, while the information in Statement (1) is NOT sufficient to answer the question.


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