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Estimation question for Mike

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Joined: 07 Apr 2012
Posts: 464
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Estimation question for Mike [#permalink] New post 21 Nov 2013, 03:26
Hi Mike,

I found this question and I tried to approximate....

What I did was approximate the selling price as 6 instead of 6.5 and got something along the lines of 6666.
Luckily I chose the answer that was closes to it, but if I had approximated to 7 instead, I may have gotten stuck
between answers D and E....

Can you help with this?

last-year-a-certain-bond-price-with-a-face-value-of-130546.html

p.s. I wrote to you in a PM and you told me to post this here :)

Thanks
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Magoosh GMAT Instructor
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Joined: 28 Dec 2011
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Kudos [?]: 3165 [1] , given: 38

Re: Estimation question for Mike [#permalink] New post 21 Nov 2013, 11:32
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Expert's post
ronr34 wrote:
Hi Mike,

I found this question and I tried to approximate....

What I did was approximate the selling price as 6 instead of 6.5 and got something along the lines of 6666.
Luckily I chose the answer that was closes to it, but if I had approximated to 7 instead, I may have gotten stuck
between answers D and E....

Can you help with this?

last-year-a-certain-bond-price-with-a-face-value-of-130546.html

p.s. I wrote to you in a PM and you told me to post this here :)

Thanks

Dear ronr34,
I'm happy to help with this. :-)
Here's the original question again.
Last year a certain bond price with a face value of 5000 yielded 8% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?

A. 4063
B. 5325
C. 5351
D. 6000
E. 6154


First of all, notice: the answer choices are far too close together for estimation. We only can use estimation when there are huge gaps between the answer choices. These tight gaps will force us to be more precise in our work.

The interest was 8% of $5000. Well, 1% of $5000 is $50, and eight times that is $400. That's the exact interest, $400. That's the easy part.

Now, essentially, we are faced with the problem of --- find the x such that 6.5% of x is $400. Hmmn. That's no picnic without a calculator, and of course, the GMAT must have had some elegant "no calculator" solution in mind: they always do! Well, let's think about backsolving. Normally, all other things being equal, we would start with (C) and work from there. See:
http://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/
Here, there are four relatively ugly choices, but one very easy choice, (D). We will start backsolving with (D). In a way, the design of the five answer choices is handing us (D) on a silver plate as the ideal candidate for backsolving.

Suppose the bond's selling price were exactly $6000. Well, 1% of that is $60. Six times that is 6%, $360. Half of one percent is 0.5%, $30. Add those two ---- 6.5% of $6000 must be 360 + 30 = $390. That's slightly less than $400. Therefore, the selling price must be greater than $6000, which immediately isolate (E) as the only possible answer.

So, you see, it's a very elegant non-calculator solution, but it doesn't involve estimations in the least. You always have to keep your problem-solving options open. The GMAT creates all kinds of clever problems, each with a different "trick" to unlock it, and you have to maintain a kind of mental agility to adjust to these ever-shifting demands.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

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Senior Manager
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Joined: 07 Apr 2012
Posts: 464
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Kudos [?]: 23 [0], given: 58

Re: Estimation question for Mike [#permalink] New post 22 Nov 2013, 01:35
mikemcgarry wrote:
ronr34 wrote:
Hi Mike,

I found this question and I tried to approximate....

What I did was approximate the selling price as 6 instead of 6.5 and got something along the lines of 6666.
Luckily I chose the answer that was closes to it, but if I had approximated to 7 instead, I may have gotten stuck
between answers D and E....

Can you help with this?

last-year-a-certain-bond-price-with-a-face-value-of-130546.html

p.s. I wrote to you in a PM and you told me to post this here :)

Thanks

Dear ronr34,
I'm happy to help with this. :-)
Here's the original question again.
Last year a certain bond price with a face value of 5000 yielded 8% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?

A. 4063
B. 5325
C. 5351
D. 6000
E. 6154


First of all, notice: the answer choices are far too close together for estimation. We only can use estimation when there are huge gaps between the answer choices. These tight gaps will force us to be more precise in our work.

The interest was 8% of $5000. Well, 1% of $5000 is $50, and eight times that is $400. That's the exact interest, $400. That's the easy part.

Now, essentially, we are faced with the problem of --- find the x such that 6.5% of x is $400. Hmmn. That's no picnic without a calculator, and of course, the GMAT must have had some elegant "no calculator" solution in mind: they always do! Well, let's think about backsolving. Normally, all other things being equal, we would start with (C) and work from there. See:
http://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/
Here, there are four relatively ugly choices, but one very easy choice, (D). We will start backsolving with (D). In a way, the design of the five answer choices is handing us (D) on a silver plate as the ideal candidate for backsolving.

Suppose the bond's selling price were exactly $6000. Well, 1% of that is $60. Six times that is 6%, $360. Half of one percent is 0.5%, $30. Add those two ---- 6.5% of $6000 must be 360 + 30 = $390. That's slightly less than $400. Therefore, the selling price must be greater than $6000, which immediately isolate (E) as the only possible answer.

So, you see, it's a very elegant non-calculator solution, but it doesn't involve estimations in the least. You always have to keep your problem-solving options open. The GMAT creates all kinds of clever problems, each with a different "trick" to unlock it, and you have to maintain a kind of mental agility to adjust to these ever-shifting demands.

Does all this make sense?
Mike :-)

Great!!
10 thumbs up :)
Re: Estimation question for Mike   [#permalink] 22 Nov 2013, 01:35
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