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13 May 2016, 05:07
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Difficulty:

65% (hard)

Question Stats:

64% (02:14) correct 36% (04:39) wrong based on 77 sessions

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John invests $x at the semi-annual constant compounded rate of 2 percent and also does$10,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
A. $20,001 B.$20,101
C. $20,201 D.$20,301
E. $20,401 * A solution will be posted in two days. [Reveal] Spoiler: OA _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons - try it yourself See our Youtube demo Kudos [?]: 3050 [0], given: 0 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 4341 Kudos [?]: 3050 [0], given: 0 GPA: 3.82 Re: John invests$x at the semi-annual constant compounded rate of 2 perce [#permalink]

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15 May 2016, 21:13
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From x(1+2%/2)^2-x=10000(1+4%/4)^4-10000, we get x(1.1^2-1)=10000(1.1^4-1)=10000(1.1^2-1)(1.1^2+1). (1.1^2-1) can be canceled out in either sides. So we get x=10000(1.1^2+1)=20,201. Hence, the correct answer is C.
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16 May 2016, 02:53
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Maybe I was just lucky on this one but here's how I solved it in 2,25 minutes without complicated math:

This will come down to decimals:

Second investment
4% per annum = 1% per quarter
$10000 * 101% =$10100
$10100 * 101% =$10201
$10201 * 101% =$10303.01
$10303.01 * 101% =$10306.0401

First investment
2% per annum = 1% per 6 month period
So the same pattern as above wil repeat.
To get a decimal of .0401 after 2 periods we need 2 in the hundreds digit.
Only (C) satisfies this constraint.

(This only works because both were compounded at the same rate - 1% per period)

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Re: John invests $x at the semi-annual constant compounded rate of 2 perce [#permalink] ### Show Tags 30 Jan 2017, 23:01 MathRevolution wrote: John invests$x at the semi-annual constant compounded rate of 2 percent and also does $10,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x?? A.$20,001
B. $20,101 C.$20,201
D. $20,301 E.$20,401

* A solution will be posted in two days.

May I am probably the only one who didnt understand the question right. I interpreted that 2% is the semi-nannual interest compounded twice each year. This way we will have final amount of x(1.02)^2 by the end of one year. However, I see that the correct solution involves x(1+(.02/2))^2. This approach tells me that the annual rate was 2% which was compounded semi-annually.

How likely is that the interpretation can be first one. I know it is the words, but is it the latter way always?

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Re: John invests $x at the semi-annual constant compounded rate of 2 perce [#permalink] ### Show Tags 27 Aug 2017, 01:41 4% compounding quarterly, i.e. 1 % per quarter $$Q_1$$ :1% of 10000 = 100 $$Q_2$$ :1% of 10000 + 1% of 100 (interest for$$Q_1$$) = 100 + 1=101 $$Q_3$$ :1% of 10000 + 1% of 100 (interest for$$Q_1$$) + 1% of 101 (interest for $$Q_2$$) = 100 + 1 + 1.01 = 102.01 $$Q_4$$ :1% of 10000 + 1% of 100 (interest for$$Q_1$$) + 1% of 101 (interest for $$Q_2$$) + 1% of 102.01 (interest for $$Q_3$$) = 100 + 1 + 1.01 + 1.0201 = 103.0301 Total interest = 100 + 101 + 102.01 + 103.0301 = 406.0401 Now using option Option A: 20001 at 2% semiannually 1%of 20001= 200.01 1%of 20001 + 1%of 200.01 = 200.01 + 2.0001 = 202.0101 Total interest = 200.01 + 202.0101 = 402.0201 which is not equal to 406.0401 Option B: 20101 Using the same pattern total interest is 201.01 + 201.01 + 2.0101 which is not equal to 406.0401 Option C: 20201 Using the same pattern total interest is 202.01 + 202.01 + 2.0201 which is equal to 406.0401 Thus answer is Option C _________________ Abhishek Parikh Math Tutor Whatsapp- +919983944321 Mobile- +971568653827 Website: http://www.holamaven.com Kudos [?]: 31 [0], given: 13 Re: John invests$x at the semi-annual constant compounded rate of 2 perce   [#permalink] 27 Aug 2017, 01:41
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