800score.com
http://www.800score.com/forum/

GMAT Algebra (Data Sufficiency)
http://www.800score.com/forum/viewtopic.php?f=3&t=120
Page 1 of 1

Author:  questioner [ Mon Jan 24, 2011 4:55 pm ]
Post subject:  GMAT Algebra (Data Sufficiency)

If ax² + bx³ = 5, where a and b are non-zero numbers, what is the value of a + b?
(1) ax² = a
(2) bx³ = b

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) The important thing to remember here is that, when a number is squared, it will always result in a positive, regardless of whether the original number was negative or positive. This is not the case with a number that is cubed. A cube will only be positive if the original integer was positive; otherwise, it will be negative. That having been said, statement (1) is insufficient. While we know that x can be nothing other than 1 or -1 in order for ax² to equal a, we are not told specifically if x is 1 or -1.

Statement (2), however, is sufficient. Because x is cubed, we know that it had to be 1 from the beginning. Statement (2) tells us that a + b = 5. The answer is (B).

For more information on this type of questions, order the online prep course by clicking the following link:
http://www.800score.com/ordercourse.html
-------------

The right answer is D.
ax² = a, so x² = 1, so x = 1. And so it is similar to statement (2).

Author:  Gennadiy [ Mon Jan 24, 2011 5:12 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

ax² = a
x² = 1
x = 1 or x = -1

If x = 1, then
ax² + bx³ = a × 1² + b × 1³ = a + b = 5

If x = -1, then
ax² + bx³ = a × (-1)² + b × (-1)³ = a – b = 5
But we don't know what a + b equals to in this case (if x = 1).

Therefore statement (1) by itself is NOT sufficient.

Author:  questioner [ Mon Feb 28, 2011 2:35 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

By default, all the numbers in GMAT are real. Therefore, both x = 1 and x = Image are valid solutions for (2). While 1 yields the right answer, Image does not. In conclusion, we have to use Statement 1 to make sure, that x = 1, not Image.

Attachments:
one_and_one_third.gif [1.28 KiB]
Not downloaded yet

Author:  Gennadiy [ Mon Feb 28, 2011 2:44 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

The values Image and 1 are equal.

The second statement yields x³ = 1. This equation has only one solution: x = ³√1 = 1.

Author:  questioner [ Thu Sep 01, 2011 12:55 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

In case of 1, if x is -1, then we get ab = 5 and when x is 1, we get a + b =5. Since we get only 1 value of a + b from (1), I feel the answer to this should be D.

Author:  Gennadiy [ Thu Sep 01, 2011 1:21 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

Quote:
Since we get only 1 value of a + b from (1)
The situation when x is -1 does NOT give us any specific value of a + b. It gives only the value of ab. This is NOT sufficient.
For example, at least two of the possible variants are:
If a = 4, b = 5, then ab = -1, a + b = 9.
If a = 5, b = 6, then ab = -1, BUT a + b = 11.

Therefore statement (1) does NOT give us a definite value of a + b.

Author:  questioner [ Tue Sep 20, 2011 5:23 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

a, b and x could be rational numbers, it is not mentioned that they are integers. Hence, the inference that x could only be 1 or -1 is wrong; e.g. x = 1/2, a = 4 and b = 32.

Author:  Gennadiy [ Tue Sep 20, 2011 5:32 pm ]
Post subject:  Re: math (test 1, question 28): algebra.

questioner wrote:
a, b and x could be rational numbers, it is not mentioned that they are integers. Hence, the inference that x could only be 1 or -1 is wrong; e.g. x = 1/2, a = 4 and b = 32.

The proposed values do NOT fit in any statement:
Statement (1) will transform into 4 × (1/2)² = 4. This is NOT correct.
Statement (2) will transform into 32 × (1/2)³ = 32. This is NOT correct.

The basic question statement does NOT specify that x is an integer, but each additional statement gives us some specific possible values of x. Statement (1) yields x = -1 and x = 1. Statement (2) yields x = 1 only.

Author:  cjuarezh [ Tue Aug 07, 2012 2:36 am ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

I desagree with the given answer, we have:

If ax² + bx³ = 5, where a and b are non-zero numbers, what is the value of a + b?
(1) ax² = a
(2) bx³ = b

I agree that with (1) we cannot answer the question, but (2) isn't enough either.

number 2 says that x³ = 1 (with b non-zero), which has 3 solutions, not 1:

x³ - 1 = 0
(x – 1) × (x² + x + 1)=0
Either (x – 1) = 0 or (x² + x + 1) = 0. Only x – 1 = 0 gives x = 1.
But the 3 solutions are:

1, -1/2 + (√3 / 2) × i, -1/2 – (√3 / 2) × i

The second and third solution, when squared, don't equal 1, so we need the first statement to know that x can't take these values. Therefore, the answer is C and not B.

Author:  Gennadiy [ Wed Aug 08, 2012 1:20 pm ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

Quote:
But the 3 solutions are:

1, -1/2 + (√3 / 2) × i, -1/2 – (√3 / 2) × i
Your solution would be true, if x were a complex variable. But x is a real variable, not a complex one.

NEVER assume in GMAT that we deal with complex numbers (variables).
ALWAYS assume that a number (variable) is a real number, if nothing else is stated.

Page 1 of 1 All times are UTC - 5 hours [ DST ]
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
http://www.phpbb.com/