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09 Jul 2012, 03:46
3
7
00:00

Difficulty:

5% (low)

Question Stats:

86% (01:27) correct 14% (01:43) wrong based on 1043 sessions

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If $5,000 invested for one year at p percent simple annual interest yields$500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?

(1) k = 0.8p
(2) k = 8

Diagnostic Test
Question: 40
Page: 26
Difficulty: 550

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52231

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09 Jul 2012, 05:06
Bunuel wrote:
If $5,000 invested for one year at p percent simple annual interest yields$500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?

(1) k = 0.8p
(2) k = 8

Hi,

Difficulty level: 600

SI (Simple Interest) = $$\frac{PRT}{100}$$,
where, P = Principal,
R = Rate in percentage,
T = Time

Thus, $$500 = \frac {5000*p*1}{100}$$
or p = 10%

New Principal invested depends on value of k

Using (1),
k=0.8*p=8%
$$P=\frac {100SI}{RT} =\frac {100*500}{8*1}$$. Sufficient.

Using (2),
k=8%
$$P=\frac {100SI}{RT} =\frac {100*500}{8*1}$$. Sufficient.

Regards,
CEO
Joined: 11 Sep 2015
Posts: 3330
Re: If $5,000 invested for one year at p percent simple annual [#permalink] Show Tags 15 Jan 2018, 09:25 Top Contributor Bunuel wrote: If$5,000 invested for one year at p percent simple annual interest yields $500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars? (1) k = 0.8p (2) k = 8 The great thing about DS questions is that we aren't required to perform calculations if we know that we COULD perform those calculations. Here's what I mean: Target question: What amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ? Given: If$5000 invested for one year at p percent simple annual interest yields $500 IMPORTANT: There's ONLY ONE possible value of p that will yield$500 interest after 1 year (if $5000 is invested). So, we COULD perform some calculations to determine that ONE VALUE of p. Statement 1: k = 0.8p Since we COULD determine the value of p, we COULD also determine the value of k Using the fact that k = 0.8p). Once we know the ONE value of k, we COULD determine how much money needs to be invested to get$500 in interest after 1 year.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k = 8
Perfect!
Once we know the value of k, we COULD determine how much money needs to be invested to get $500 in interest after 1 year. Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer = D Cheers, Brent _________________ Test confidently with gmatprepnow.com Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2830 Re: If$5,000 invested for one year at p percent simple annual  [#permalink]

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17 Jun 2018, 19:05
Bunuel wrote:
If $5,000 invested for one year at p percent simple annual interest yields$500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?

(1) k = 0.8p
(2) k = 8

Since interest amount = principal x interest rate x time, we have:

500 = 5000 x p/100 x 1

500 = 50 x p

p = 10

Let A = principal that yields $500 interest at k percent simple annual interest rate in one year, so we have: 500 = A x k/100 x 1 50000/k = A So if we know the value of k, we can determine the value of A. Statement One Alone: k=0.8p Since p = 10, then k = 0.8(10) = 8. Since we know the value of k, we can determine the value of A (without actually determining it). Statement one alone is sufficient. Statement Two Alone: k=8 Since we know the value of k, we can determine the value of A (without actually determining it). Statement two alone is sufficient. Answer: D _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: If$5,000 invested for one year at p percent simple annual &nbs [#permalink] 17 Jun 2018, 19:05
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