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

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If positive integer a doubles, which of the following must decrease?  [#permalink]

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New post 20 Mar 2019, 10:05
1
1
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A
B
C
D
E

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  25% (medium)

Question Stats:

80% (01:25) correct 20% (01:17) wrong based on 30 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
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If positive integer a doubles, which of the following must decrease?  [#permalink]

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New post 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.

So answer is a

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Re: If positive integer a doubles, which of the following must decrease?  [#permalink]

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New post 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
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Re: If positive integer a doubles, which of the following must decrease?   [#permalink] 06 Apr 2019, 03:01
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If positive integer a doubles, which of the following must decrease?

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