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# a% of b is increased by a%.

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Retired Moderator
Joined: 27 Oct 2017
Posts: 1787
WE: General Management (Education)
a% of b is increased by a%.  [#permalink]

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14 Mar 2020, 18:09
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35% (medium)

Question Stats:

79% (01:12) correct 21% (01:53) wrong based on 29 sessions

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GMATBusters’ Quant Quiz Question -2

a% of b is increased by a%. what is the result in terms of a and b?
A) 100ab+a
B) ab + a/100
C) 100ab + a/100
D) 100ab + ab/100
E) ab(a+100)/10000

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Retired Moderator
Joined: 27 Oct 2017
Posts: 1787
WE: General Management (Education)
Re: a% of b is increased by a%.  [#permalink]

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14 Mar 2020, 18:10

Official Solution

a% of b is increased by a%. what is the result in terms of a and b?
a% of b = ab/100
increasing by a% = multiplying by (1+a/100)
hence result is ab/100 * (1+a/100)
= ab(a+100)/10000
E
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Director
Joined: 22 Feb 2018
Posts: 741
Re: a% of b is increased by a%.  [#permalink]

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14 Mar 2020, 18:21
a% of b is increased by a%. what is the result in terms of a and b?
A) 100ab+a
B) ab + a/100
C) 100ab + a/100
D) 100ab + ab/100
E) ab(a+100)/10000

a/100 * b + a/100 * ab/100
ab/100 (1 + a/100)
ab/100 (100+a/100)
ab (100+a)/10000
Imo. Ans. E
Senior Manager
Joined: 31 May 2017
Posts: 412
Re: a% of b is increased by a%.  [#permalink]

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14 Mar 2020, 19:06
Lets substitute numbers for a and b

Let A = 10 , B = 100

Step 1:
a% of b is increased by a%. Based on our numbers , 10% of 100 is increased by 10%. 10% 100 is 10 which is increased by 10% again. so we have 11.

Step 2:
What is result in terms of a and b.

Basically we need to find "11 is what in terms of 10 and 100". When we substitute each answer option, we get E as the answer.

Ans: E
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Joined: 18 Dec 2017
Posts: 1364
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: a% of b is increased by a%.  [#permalink]

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14 Mar 2020, 20:06
Quote:
a% of b is increased by a%. what is the result in terms of a and b?
A) 100ab+a
B) ab + a/100
C) 100ab + a/100
D) 100ab + ab/100
E) ab(a+100)/10000

Let's play with numbers first :
a% of b is increased by a%.

Lets say b is 100. a is 20. So 20% of 100 is 20. Cool.

Increase 20 by 20% we get 24.

Let's go to options.

A) 100ab+a - This value will result in a very high value so clearly not the right choice.
B) ab + a/100 - Same as choice A.
C) 100ab + a/100 - Same as Choice A
D) 100ab + ab/100 - Same as Choice A
E) ab(a+100)/10000 -
$$(100*20(120)/10000)$$
$$1*2*12$$
$$24$$

Approach 2 : Algebra
a% of b = ab/100
Increase by a%. This means take the a% of original number and add the value to it.

$$(ab/100) + ((a/100) * (ab/100))$$
$$(ab/100) + (a*ab/100*100)$$
$$(ab/100) + (a^2*b/10000)$$
$$(100ab+a^2*b/10000)$$
$$(ab(100+a)/10000)$$

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Joined: 18 Jan 2020
Posts: 291
Re: a% of b is increased by a%.  [#permalink]

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14 Mar 2020, 20:40
OA is supposedly B
As A% of B is increased by a%
And B option is the only feasible option defining relationship between a and b

Posted from my mobile device
Manager
Joined: 10 Jun 2018
Posts: 54
Re: a% of b is increased by a%.  [#permalink]

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14 Mar 2020, 23:55
a% of b = $$\frac{ab}{100}$$
This is increased by a% so final result would be:
$$\frac{ab}{100}$$+$$\frac{a}{100}*(\frac{ab}{100})$$
= $$\frac{100ab+a^2 b}{10000}$$
=$$\frac{ab(100+a)}{10000}$$

Option E
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Re: a% of b is increased by a%.  [#permalink]

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15 Mar 2020, 01:17
Given: a% of b is increased by a%.

Asked: what is the result in terms of a and b?

a% of b = ab/100
ab/100 is increased by a%, the result = ab/100 (1+a/100) = ab(100+a)/10000

A) 100ab+a
B) ab + a/100
C) 100ab + a/100
D) 100ab + ab/100
E) ab(a+100)/10000

IMO E
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Re: a% of b is increased by a%.  [#permalink]

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15 Mar 2020, 02:55

b X a/100(1+a/100)
=ab(100+a)/10000
Re: a% of b is increased by a%.   [#permalink] 15 Mar 2020, 02:55