If ab ≠ 0; is a/b 0 ? (1) |a*b| = a*b (2) |a| + |b| = |a + b |

Question

If  ab 
eq{0} ; is  \frac{a}{b} > 0 ?

(1) |ab| = ab

(2) |a| + |b| = |a + b|

historyfan10 · Answer

I have a question: why is statment 2 wrong?

if I have the numbers a= -5 and b =-2

I get: |-5|+|-2|=|-5-2|
= 5+2=|-7|
= 7=7

and -5/-2 = 5/2>0

should this not also be correct?

AndrewN · Answer

Hello,  historyfan10 . I am not sure if the OA given earlier was incorrect, but Statement 2 is SUFFICIENT on its own. Since you know that neither  a  nor  b  can be 0, they must either both be positive or negative for the equation to hold; either way, it  must  be true that the quotient in question will be positive, or greater than 0. Since either Statement 1 or 2 is SUFFICIENT alone, choice (D) is the correct answer.

Was the earlier OA something other than (D)?

- Andrew

TestPrepUnlimited · Answer

\frac{a}{b}  is greater than 0 as long as  a  and  b  have the same sign. Therefore we are asking if they have the same sign.

Statement 1:

This tells us a*b is positive. Thus a and b must have the same sign. Sufficient.

Statement 2:

Again the concern is whether a and b have the same sign. We get a + b = a + b if both positive, or (-a) + (-b) = (-a - b) if both negative, so the equation holds. If we have opposite signs such as a = 2 and b = -2, the equation turn into 2 + 2 = 0 so this tells us a and b must have the same sign. Sufficient.

Ans: D

Pixelm · Answer

Hello, can someone explain what are the answer choices please?

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.

If ab ≠ 0; is a/b > 0 ? (1) |ab| = ab (2) |a| + |b| = |a + b |

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GMAT Data Sufficiency (DS) Questions

If ab ≠ 0; is a/b > 0 ? (1) |a*b| = a*b (2) |a| + |b| = |a + b |