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The difference between the value of a number increased by 25

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anilnandyala
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The difference between the value of a number increased by 25 [#permalink] New post  20 Dec 2010, 09:11
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The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90
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BrentGMATPrepNow
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The difference between the value of a number increased by 25 [#permalink] New post  Updated on: 17 May 2021, 07:17
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anilnandyala wrote:
The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90


Let x = the original number

Value of the number INCREASED by 25% = 1.25x
Value of the number DECREASED by 30% = 0.7x

DIFFERENCE = 22
So, 1.25x - 0.7x = 22
Simplify: 0.55x = 22
So, x = 22/0.55

NOTE: We need not calculate 22/0.55
Notice that 22/0.5 = 44
Since 0.55 is a little bit BIGGER than 0.5, we can conclude that 22/0.55 will be a little bit SMALLER than 44

Answer: A

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Originally posted by BrentGMATPrepNow on 30 Mar 2017, 09:01.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:17, edited 2 times in total.
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Bunuel
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Re: the differance between the value of a number [#permalink] New post  20 Dec 2010, 09:15
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anilnandyala wrote:
the differance between the value of a number increased by 25% and the value of the original number decreased by 30% is 22 what is the original number?

40
50
65
70
90


Let the original # be \(x\) then \(1.25x-0.7x=22\) --> \(x=40\).

Answer: A.
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Re: The difference between the value of a number increased by 25 [#permalink] New post  17 May 2017, 14:37
The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90

Let the number be x.
Number increased by 25% = 125% of x = 1.25x
Original number decreased by 30% = 70% of x = 0.7x
Difference between values = 1.25x - 0.7x = 22, 0.55x = 22
x = 22/0.55 = 40
Answer A...

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Re: The difference between the value of a number increased by 25 [#permalink] New post  19 Oct 2018, 15:20
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anilnandyala wrote:
The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

A. 40
B. 50
C. 65
D. 70
E. 90


We can let n = the original number and create the equation:

1.25n - 0.7n = 22

0.55n = 22

n = 40

Answer: A
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Pratap24
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The difference between the value of a number increased by 25 [#permalink] New post  08 Oct 2021, 01:46
25% here means 5/4 and 30% means 7/10
So, 5/4x-7/10x=22
11x=440 (on solving)
x=40

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Re: The difference between the value of a number increased by 25 [#permalink] New post  25 Oct 2022, 12:28
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