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Absolute value question from Kaplan

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Absolute value question from Kaplan [#permalink]

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New post 05 Oct 2017, 12:42
00:00
A
B
C
D
E

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
[Reveal] Spoiler: OA

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Absolute value question from Kaplan [#permalink]

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New post 05 Oct 2017, 16:39
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

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Absolute value question from Kaplan [#permalink]

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New post 05 Oct 2017, 17:32
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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

Glad you posted, ari.banerjee :-)

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

Answer D

Does that help? If not, could you be a little more specific about what does not make sense?

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Re: Absolute value question from Kaplan [#permalink]

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New post 05 Oct 2017, 19:08
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

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Re: Absolute value question from Kaplan [#permalink]

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New post 05 Oct 2017, 20:53
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: https://gmatclub.com/forum/if-m-5-1-the ... 03336.html

Please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html

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Kudos [?]: 132588 [0], given: 12326

Re: Absolute value question from Kaplan   [#permalink] 05 Oct 2017, 20:53
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Absolute value question from Kaplan

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