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OG Q - Day 5

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Manonamission: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Mon Aug 01, 2016 9:54 amFollowed by: 1 member

by Manonamission » Sun Sep 04, 2016 7:35 am

Hello Guys,

I am following 60 day schedule and the below Q is with respect to that only. I would like to seek help or discuss Qs which I went wrong in the stipulated time of 2 mins. I am also practicing the method of guessing work in the process.

1. If the quotient a/b is positive, which of the following must be true?

(A) a>0
(B) b>0
(0 ab>0
(D) a-b>0
(E) a + b>0

regards,
MoM

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Source: Beat The GMAT — Quantitative Reasoning | Sun Sep 04, 2016 7:35 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Sun Sep 04, 2016 8:51 am

Manonamission wrote:

Hello Guys,

I am following 60 day schedule and the below Q is with respect to that only. I would like to seek help or discuss Qs which I went wrong in the stipulated time of 2 mins. I am also practicing the method of guessing work in the process.

1. If the quotient a/b is positive, which of the following must be true?

(A) a>0
(B) b>0
(C) ab>0
(D) a-b>0
(E) a + b>0

regards,
MoM

Two approaches: 1) Use logic. If a/b is positive then a and b are either both positive or both negative. If you multiply two positives together or two negatives together, you'll get a positive number. So C is correct.

2) Pick simple numbers. If a= -1 and b = -1, only C will work.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Sep 04, 2016 11:38 am

Hi MoM,

As you continue to study, it's beneficial to 'build up' more than one set of skills. Most GMAT questions are designed so that they can be solved in more than one way, so it's valuable to redo questions using different methods (even if you correctly answered the question on the first try).

This question is built around Number Properties (which is a subject that is heavily represented in the Quant section - especially in DS). If you have the proper Number Property knowledge, then you can beat this question without having to do too much work (although you'll still want to take notes so that you can avoid making little mistakes). You can also solve it by TESTing VALUES.

We're told that A/B is POSITIVE. This means that both variables have the same 'sign' (they're either both positive OR both negative). Keeping both possibilities in mind is important because the question asks what MUST be true (which means "which is ALWAYS TRUE no matter how different examples you can come up with).

Knowing that the two variables COULD both be negative would allow you to immediately eliminate 3 answers: A, B and E. Taking that logic one step further, you probably already know that (positive)(positive) = positive and (negative)(negative) = positive, so one of the remaining two answers is clearly the correct one...

Final Answer: C

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Rich

Contact Rich at [email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Sep 29, 2016 5:55 pm

A little algebra is also fine here:

a/b > 0

If b > 0, then multiplying both sides by b gives: a > 0

So we could have a > 0, b > 0.

If b < 0, then multiplying both sides by b gives: a < 0.

So we could have a < 0, b < 0.

That tells us we're got BOTH positive or BOTH negative, which is the same as option C.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Sep 29, 2016 5:56 pm

The other option here is to pick a few sets of numbers that satisfy the prompt, that find the only answer that works for ALL of them.

If a/b > 0, we could have

a = 1, b = 3
a = -1, b = -3
a = 3, b = 1
a = -3, b = -1

and only C fits all four!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8142; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Apr 04, 2018 4:58 pm

If the quotient a/b is positive, which of the following must be true?

(A) a>0
(B) b>0
(0 ab>0
(D) a-b>0
(E) a + b>0

We are given that the quotient a/b is positive (i.e., greater than zero). We know that in division when a quotient is positive, the two numbers being divided are either both negative or both positive.

This is also the case in multiplication; that is, to get a product that is positive, we must multiply two positive numbers or two negative numbers. Thus, the only answer choice that MUST be positive is C, ab > 0.

Answer: C

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