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# Absolute value question from Kaplan

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Intern
Joined: 31 Mar 2017
Posts: 10
Concentration: Strategy, Finance
GPA: 4
Absolute value question from Kaplan  [#permalink]

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05 Oct 2017, 11:42
00:00

Difficulty:

(N/A)

Question Stats:

90% (00:21) correct 10% (00:26) wrong based on 10 sessions

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Hello Guys,
This is my first qs post here. I came across this problem and the answer explaination doesnt make any sense. Can someone please give me a good reason to the answer?

If |m/5|>1, then which of the following must be true?

a) m>5
b) m<5
c) m=5
d) m not equal to 5
e) m<-5

Thank you,
Ari

--== Message from the GMAT Club Team ==--

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Joined: 15 May 2017
Posts: 197
Absolute value question from Kaplan  [#permalink]

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05 Oct 2017, 15:39
ari.banerjee wrote:
Hello Guys,
This is my first qs post here. I came across this problem and the answer explaination doesnt make any sense. Can someone please give me a good reason to the answer?

If |m/5|>1, then which of the following must be true?

a) m>5
b) m<5
c) m=5
d) m not equal to 5
e) m<-5

Thank you,
Ari

The solution set to this problem is that |m| is greater than 5. i.e. 7 or -7 both satisfy this equation. A,B,E, are all possible solutions to the equations, but not the only solution so we can't say any of them must be true. For example, if m = -7, A is not true or if m is 7, B and E are not true. C is not true, because the equation states that m/5 cannot be equal to 1. Therefore, the solution has to be D. D is the only answer that is true under ALL SOLUTIONS for this equation. D satisfies 7 and -7, and any other possible number in the solution
Senior SC Moderator
Joined: 22 May 2016
Posts: 2095
Absolute value question from Kaplan  [#permalink]

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05 Oct 2017, 16:32
1
ari.banerjee wrote:
Hello Guys,
This is my first qs post here. I came across this problem and the answer explaination doesnt make any sense. Can someone please give me a good reason to the answer?

If |m/5|>1, then which of the following must be true?

a) m>5
b) m<5
c) m=5
d) m not equal to 5
e) m<-5

Thank you,
Ari

Expanding a bit on cxa0897 's good answer; my focus is CAN vs. MUST

It's an interesting question. It could boggle if you think too much.

The crucial distinction:
CAN vs. MUST it be true?
We are looking for the latter.

$$|\frac{m}{5}| > 1$$. Solve for m

Case One: $$\frac{m}{5} > 1$$, so $$m > 5$$

Case Two: $$\frac{m}{5} < -1$$, so $$m < -5$$

$$m > 5$$ OR $$m < -5$$

Which of the following MUST be true?

A) m>5: Can be true.
If m = 10, $$|\frac{10}{5}| > 1$$

MUST it be true? No.
If m = -10, then
m is NOT greater than 5, but
$$|\frac{-10}{5}|$$ is > 1
Can, not must. REJECT

B) m<5: can be true
If m < - 5, |-10/2| > 1

But can be FALSE. This choice violates the excluded interval from -5 to 5.
If m = 3:$$|\frac{3}{5}| < 1$$. REJECT

c) m=5: CANNOT be true. $$\frac{5}{5}$$ equals 1. The result should be greater than 1. REJECT

d) m not equal to 5: MUST be true.
$$\frac{5}{5}= 1$$, and 1 will never be greater than 1.

MUST be true is the logical converse of Answer C, stated a little more strongly.

From reasoning in C, where 5/5 equals 1: that result is never going to be greater than 1. Hence m can never = 5. $$m$$ not equal to 5 MUST be true. KEEP

e) m<-5: same as (A)

Can be true
If m = -10, |-10/5| > 1

MUST be true? No.
When m = 10
|10/2| > 1, but
10 is not less than -5. REJECT

Does that help? If not, could you be a little more specific about what does not make sense?
Manager
Joined: 30 Aug 2017
Posts: 87
Location: Korea, Republic of
GMAT 1: 700 Q51 V31
GPA: 3.68
Re: Absolute value question from Kaplan  [#permalink]

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05 Oct 2017, 18:08
I think A, D, E also be "must be true"

Sujan, Jack, and Mike are my family --> Mike is my family (must be true)
M>5 or M<-5 --> M>5 (must be true)
M<-5 (must be true)
of course M not equal to 5 must be true
Math Expert
Joined: 02 Sep 2009
Posts: 50616
Re: Absolute value question from Kaplan  [#permalink]

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05 Oct 2017, 19:53
ari.banerjee wrote:
Hello Guys,
This is my first qs post here. I came across this problem and the answer explaination doesnt make any sense. Can someone please give me a good reason to the answer?

If |m/5|>1, then which of the following must be true?

a) m>5
b) m<5
c) m=5
d) m not equal to 5
e) m<-5

Thank you,
Ari

Discussed here: if-m-5-1-then-which-of-the-following-must-be-true-103336.html

TOPIC IS LOCKED AND ARCHIVED.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: Absolute value question from Kaplan &nbs [#permalink] 05 Oct 2017, 19:53
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