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a% of b is increased by a%.

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a% of b is increased by a%.  [#permalink]

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New post 14 Mar 2020, 18:09
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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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Re: a% of b is increased by a%.  [#permalink]

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New post 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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Re: a% of b is increased by a%.  [#permalink]

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New post 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
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Re: a% of b is increased by a%.  [#permalink]

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New post 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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Re: a% of b is increased by a%.  [#permalink]

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New post 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 -
\((100*20(120)/10000)\)
\(1*2*12\)
\(24\)

Answer E.

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.

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

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

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New post 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

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

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New post 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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New post 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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New post 15 Mar 2020, 02:55
Answer :E

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

a% of b is increased by a%.

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