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# If positive integer m were increased by 20%, decreased by 2

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Retired Moderator
Joined: 07 Jun 2014
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If positive integer m were increased by 20%, decreased by 2 [#permalink]  11 Jun 2018, 15:56
Expert's post
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Question Stats:

100% (00:29) correct 0% (00:00) wrong based on 10 sessions
If positive integer m were increased by 20%, decreased by 25%, and then increased by 60%, the resulting number would be what percent of m?

[Reveal] Spoiler: OA
144

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Sandy
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Active Member
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Re: If positive integer m were increased by 20%, decreased by 2 [#permalink]  13 Jun 2018, 22:45
sandy wrote:
If positive integer m were increased by 20%, decreased by 25%, and then increased by 60%, the resulting number would be what percent of m?

[Reveal] Spoiler: OA
144

let m = 100.

Now m is increased by 20% = 1.2 (100) = 120

and decreased by 25% =? 3/4 (120) = 90.

this value is increased by 60% => 90+60%(90) = 144.

144 = what % ( 100).

144-100/100 = 44%.

Sandy is the answer is 144 or 44% ? please explain me.
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037 [1] , given: 394

Re: If positive integer m were increased by 20%, decreased by 2 [#permalink]  14 Jun 2018, 04:19
1
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Expert's post
Explanation

If m were increased by 20%, decreased by 25%, and then increased by 60%, it would be multiplied by 1.2, then 0.75, then 1.6.

Since (1.2)(0.75)(1.6) = 1.44, doing these manipulations is the same as increasing by 44%, or taking 144% of a number (this is true regardless of the value of m).

Alternatively, pick a real value for m.

Because this is a percent problem, 100 is a good number to pick. First, 100 is increased by 20%: (100)(1.2) = 120.

Next, 120 is decreased by 25%, which is the same as multiplying by 75%: (120)(0.75) = 90.

Finally, 90 is increased by 60%: (90)(1.6) = 144. The new number is 144 and the starting number was 100, so the new number is$$\frac{144}{100}$$ % of the original number, or 144%.
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Sandy
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Re: If positive integer m were increased by 20%, decreased by 2   [#permalink] 14 Jun 2018, 04:19
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