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If positive integer a doubles, which of the following must decrease?

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Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 441
If positive integer a doubles, which of the following must decrease?  [#permalink]

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20 Mar 2019, 10:05
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25% (medium)

Question Stats:

74% (01:24) correct 26% (01:20) wrong based on 35 sessions

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If positive integer a doubles, which of the following must decrease?

I. $$\frac{5}{a}$$

II. $$\frac{a-5}{a}$$

III. $$5a+\frac{1}{a}$$

A) I only
B) III only
C) I and III only
D) II and III only
E) I, II, and III
Manager
Joined: 11 Feb 2013
Posts: 230
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
If positive integer a doubles, which of the following must decrease?  [#permalink]

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21 Mar 2019, 13:17
If a is doubled, it is 2a
Since a is a positive integer, both sides can be multiplied by a without impacting the sign.
i.
(5/a) [] {5/(2a)}
Multiplying both sides by 2a, it becomes
10[] 5
So 10 > 5.
Here DOUBLING reduces the value.

Now check (iii) which is available in almost every options
{5a+1/a} [] {10a+1/(2a)}
Reducing 5a +1/a, it becomes
0 [] { 5a-1/(2a)}
For any positive integer, { 5a-1/(2a)} >0
If x =1, the value of { 5a-1/(2a)} is 4.5 .
Similarly, the higher the positive integer value of a, the higher value of 5a & the lower value of { 1/(2a)}, resulting in higher value of { 5a-1/(2a)}
This, 0 < { 5a-1/(2a)}.
Here DOUBLING increases the value.
SO iii IS OUT.
That means b,c, d & e gone.

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Intern
Joined: 22 May 2018
Posts: 49
Re: If positive integer a doubles, which of the following must decrease?  [#permalink]

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06 Apr 2019, 03:01
2
Take a=5, doubling 'a' would give 10.

1. when a =5, 5/5=1
when a=10, 5/10=0.5
Value reduced.

2. when a=5, (5-5)/5=0
when a=10, (10-5)/10=0.5
value increased.

3.when a=5, 25+1/5=25.2
when a = 10, 50+1/10=50.1
Value increased.

So, only 1 is true
Re: If positive integer a doubles, which of the following must decrease?   [#permalink] 06 Apr 2019, 03:01
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