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# A man invested two equal sums of money in two banks at simple interest

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
A man invested two equal sums of money in two banks at simple interest  [#permalink]

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27 Sep 2018, 05:38
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Difficulty:

55% (hard)

Question Stats:

63% (02:38) correct 38% (03:30) wrong based on 32 sessions

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A man invested two equal sums of money in two banks at simple interest, one offering annual rate of interest of 10% and the other, at a rate of 20%. If the difference between the interests earned after two years is between $120 and$140, exclusive, which of the following could be the difference between the amounts earned for the same amounts of money, invested at the same rates of interest as above, but at compound interest?

(A) $130 (B)$135
(C) $137 (D)$154
(E) $162 _________________ CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2974 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) A man invested two equal sums of money in two banks at simple interest [#permalink] ### Show Tags 27 Sep 2018, 07:28 Bunuel wrote: A man invested two equal sums of money in two banks at simple interest, one offering annual rate of interest of 10% and the other, at a rate of 20%. If the difference between the interests earned after two years is between$120 and $140, exclusive, which of the following could be the difference between the amounts earned for the same amounts of money, invested at the same rates of interest as above, but at compound interest? (A)$130
(B) $135 (C)$137
(D) $154 (E)$162

Difference of interest after 1 year = 20%-10% = 10% of principal
Difference of interest after 2 years = 40%-20% = 20% of principal

i.e. 20% of half of the sum is between 120 and 140
i.e. Sum is between 1200 and 1400

For 1200 distributed in two accounts with sum 600 each
Interest @ 10% after two years $$= (1.1)^2*600-600 = 126$$
Interest @ 20% after two years $$= (1.2)^2*600-600 = 264$$
Difference = 138

For 1400 distributed in two accounts with sum 700 each
Interest @ 10% after two years $$= (1.1)^2*700-700 = 147$$
Interest @ 20% after two years $$= (1.2)^2*700-700 = 161$$

Only value available in options that falls between 147 and 161 is 154 hence

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Re: A man invested two equal sums of money in two banks at simple interest  [#permalink]

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30 Sep 2018, 00:03
Bunuel wrote:
A man invested two equal sums of money in two banks at simple interest, one offering annual rate of interest of 10% and the other, at a rate of 20%. If the difference between the interests earned after two years is between $120 and$140, exclusive, which of the following could be the difference between the amounts earned for the same amounts of money, invested at the same rates of interest as above, but at compound interest?

(A) $130 (B)$135
(C) $137 (D)$154
(E) $162 Responding to a pm: The difference between the interests earned in two years is in the range$120 - $140. So the answer will be obtained in a range too. We need to find the value that falls in this range. Let's take the middle value and find the value closest to it. Take the difference in SI of two years to be say$130. So each year extra SI will be $65 (because rate in second case is 20%, 10% more than the rate of 10%).$65 is 10% of the principal so principal would be $650. Diff in interest earned in CI on$650 at 10% interest vs 20% interest:
On $650, CI earned at 10% in 2 years = 65 + 65 + 6.5 On$650, CI earned at 20% in 2 years = 130 + 130 + 26
The difference is about $150.$150 is going to lie in the middle of our acceptable range so $154 should certainly lie in this range. Answer (D) _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Director Joined: 24 Nov 2016 Posts: 578 Location: United States A man invested two equal sums of money in two banks at simple interest [#permalink] ### Show Tags Updated on: 25 Aug 2019, 03:56 Bunuel wrote: A man invested two equal sums of money in two banks at simple interest, one offering annual rate of interest of 10% and the other, at a rate of 20%. If the difference between the interests earned after two years is between$120 and $140, exclusive, which of the following could be the difference between the amounts earned for the same amounts of money, invested at the same rates of interest as above, but at compound interest? (A)$130
(B) $135 (C)$137
(D) $154 (E)$162

simple interest earned: principal•years•rate_p.a.%
compound interest earned: principal(1+rate.a.%)^years-principal
compound interest earned 2 years:
[interest earned 1 year] + [interest earned 2 year]
[p(r)]+[p(r)+p(r)(r)] = [pr]+[pr(1+r)] = pr(2+r)

find principal range: 600<p<700
120<p2(20%)-p2(10%)<140… 120<p2(20%-10%)<140… 600<p<700

find low compound range: 264-126=138
[600*.2] + [600*.2+120*.2] = 120+120+24 = 264
[600*.1] + [600*.1+60*.1] = 60+60+6 = 126

find high compound range: 308-147=161
[700*.2] + [700*.2+140*.2] = 140+140+28 = 308
[700*.1] + [700*.1+70*.1] = 70+70+7 = 147

difference must be between: 138 to 161

Originally posted by exc4libur on 15 Aug 2019, 09:20.
Last edited by exc4libur on 25 Aug 2019, 03:56, edited 1 time in total.
Manager
Joined: 03 Sep 2018
Posts: 173
A man invested two equal sums of money in two banks at simple interest  [#permalink]

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25 Aug 2019, 01:01
$$120<\frac{(A*20*2)}{100}-\frac{(A*10*2)}{100}<140$$

$$600<A<700$$

$$600(1.44-1.21)<X<700(1.44-1.21)$$

$$6*23<X<7*23$$
Manager
Joined: 03 Sep 2018
Posts: 173
Re: A man invested two equal sums of money in two banks at simple interest  [#permalink]

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25 Aug 2019, 01:08
Another way:

$$600<A<700$$

$$600*0.2*2+600*0.2*0.2-600*0.1*2+600*0.1*0.1=23*6=138$$

$$700*0.2*2+700*0.2*0.2-700*0.1*2+700*0.1*0.1=23*7=161$$

$$138<X<161$$
Re: A man invested two equal sums of money in two banks at simple interest   [#permalink] 25 Aug 2019, 01:08
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