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# Grace makes an initial deposit of x dollars into a savings a

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Grace makes an initial deposit of x dollars into a savings a [#permalink]

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15 Nov 2011, 15:42
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95% (hard)

Question Stats:

47% (02:30) correct 53% (01:49) wrong based on 243 sessions

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Grace makes an initial deposit of x dollars into a savings account with a z percent interest rate, compounded annually. On the same day, Georgia makes an initial deposit of y dollars into a savings account with a z percent annual interest rate, compounded quarterly. Assuming that neither Grace nor Georgia makes any other deposits or withdrawals and that x, y, and z are positive numbers no greater than 50, whose savings account will contain more money at the end of exactly one year?

(1) z = 4
(2) 100y = zx
[Reveal] Spoiler: OA

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Last edited by Bunuel on 18 Apr 2014, 04:33, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Grace and its deposit [#permalink]

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15 Nov 2011, 18:14
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B.

B is sufficient due to the constraints in the problem. Since no number can be greater than 50 and Z is the same for both.

100y =zx

Basically says that X is larger than Y. The differences between annual and quarterly compounding of an identical interest rate over only one year will be fairly negligible. Assuming Z = 50 which is the most it can equal we are left with 2y = x. So we know that Grace is going to have more money than Georgia at the end of year 1.

Statement 2 is sufficient.

Hope that helps.
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Re: Grace and its deposit [#permalink]

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16 Nov 2011, 21:21
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enigma123 wrote:
Grace makes an initial deposit of x dollars into a savings account with a z percent interest rate, compounded annually. On the same day, Georgia makes an initial deposit of y dollars into a savings account with a z percent annual interest rate, compounded quarterly. Assuming that neither Grace nor Georgia makes any other deposits or withdrawals and that x, y, and z are positive numbers no greater than 50, whose savings account will contain more money at the end of exactly one year?
(1) z = 4
(2) 100y = zx

Responding to a pm:

Actually, u0422811's solution is perfect. That is exactly what went through my mind when I read this question.
Quarterly compounding yields more than annual compounding but the difference is minuscule in % terms.
e.g. if you invest $10 at 10% annual compounding, you get$11 at the end of the year.
but if you invest $10 at 10% quarterly compounding, you get$11.038 at the end of the year.
You get a small fraction of interest extra.

So x is invested at annual compounding and y at quarterly compounding. If x=y, the amount received from y will be a little more.

Statement 1 tells us z = 4. We need to compare x with y so this is not sufficient.

Statement 2 tells us 100y = zx
x/y = 100/z
Since maximum value of z is 50, x is at least twice of y.
If z% = 50%, amount obtained from x is 1.5x (= 3y) and that obtained from y is a little more than 1.5y.
Definitely an investment of $x results in a higher amount at the end of the year. Answer (B) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Grace and its deposit [#permalink]

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18 Apr 2014, 02:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Grace and its deposit [#permalink]

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08 Jun 2014, 10:44
VeritasPrepKarishma wrote:
enigma123 wrote:
Grace makes an initial deposit of x dollars into a savings account with a z percent interest rate, compounded annually. On the same day, Georgia makes an initial deposit of y dollars into a savings account with a z percent annual interest rate, compounded quarterly. Assuming that neither Grace nor Georgia makes any other deposits or withdrawals and that x, y, and z are positive numbers no greater than 50, whose savings account will contain more money at the end of exactly one year?
(1) z = 4
(2) 100y = zx

Responding to a pm:

Actually, u0422811's solution is perfect. That is exactly what went through my mind when I read this question.
Quarterly compounding yields more than annual compounding but the difference is minuscule in % terms.
e.g. if you invest $10 at 10% annual compounding, you get$11 at the end of the year.
but if you invest $10 at 10% quarterly compounding, you get$11.038 at the end of the year.
You get a small fraction of interest extra.

So x is invested at annual compounding and y at quarterly compounding. If x=y, the amount received from y will be a little more.

Statement 1 tells us z = 4. We need to compare x with y so this is not sufficient.

Statement 2 tells us 100y = zx
x/y = 100/z
Since maximum value of z is 50, x is at least twice of y.
If z% = 50%, amount obtained from x is 1.5x (= 3y) and that obtained from y is a little more than 1.5y.
Definitely an investment of $x results in a higher amount at the end of the year. Answer (B) Hi Karishma, taking B into consideration, we can have x=2, y=1, z=50. so X after one year will be 3. Y after one year and 4 interest bumps will be over 3.... Can you explain this? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7377 Location: Pune, India Followers: 2288 Kudos [?]: 15130 [0], given: 224 Re: Grace and its deposit [#permalink] ### Show Tags 08 Jun 2014, 22:54 ronr34 wrote: Hi Karishma, taking B into consideration, we can have x=2, y=1, z=50. so X after one year will be 3. Y after one year and 4 interest bumps will be over 3.... Can you explain this? How did you get that "Y after one year and 4 interest bumps will be over 3"? If initial investment is$1 with an annual rate of 50% compounded quarterly, at the end of the year, the amount is 1(1 + 50/400)^4 = 1.608 i.e. somewhat above 1.5. How is it 3? Note that 50% is annual rate. If it is compounded quarterly, the quarterly rate becomes 50/4%
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 15477 Followers: 651 Kudos [?]: 209 [0], given: 0 Re: Grace makes an initial deposit of x dollars into a savings a [#permalink] ### Show Tags 23 Aug 2015, 14:06 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15477 Followers: 651 Kudos [?]: 209 [0], given: 0 Re: Grace makes an initial deposit of x dollars into a savings a [#permalink] ### Show Tags 20 Nov 2016, 06:54 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Grace makes an initial deposit of x dollars into a savings a [#permalink] 20 Nov 2016, 06:54 Similar topics Replies Last post Similar Topics: 1 Steve deposited$100 to open a savings account. If there are no other 1 26 Apr 2017, 21:22
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