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Math noob. Arithmetic - Percent Strategy

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Math noob. Arithmetic - Percent Strategy

by pdonaldson1990 » Wed Feb 17, 2016 7:14 pm
Good evening,

I am fairly new to studying for the GMAT and I haven't paid any real attention to math since college algebra.... six years or so ago now. Anyhow, I came across a problem and explanation in the OG16 book which I would like to devise a strategy for and others like it:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

A) $10,350
B) $10,395
C) $10,500
D) $11,500
E) $12,705

The correct answer is B.

The book gave the following strategy:

10,000(1.10)(1.05)(.90)=10,395

My question is, are there any fast strategies to deal with this rather than multiply these numbers out?

Thank you in advance.

-Patrick
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by Brent@GMATPrepNow » Wed Feb 17, 2016 7:32 pm
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705
Start: $10,000

First year +10%
10% of $10,000 = $1000
So, we get $10,000 + $1000 = $11,000

Second year +5%
5% of $11,000 = $550
So, we get $11,000 + $550 = $11,550

Third year -10%
10% of $11,550 = $1,155
So, we get $11,550 - $1155 = [spoiler]$10,395[/spoiler]

Answer: B

Aside: We have a free video on mentally calculating x% of y: https://www.gmatprepnow.com/module/gmat- ... video/1076

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by Brent@GMATPrepNow » Wed Feb 17, 2016 7:34 pm
pdonaldson1990 wrote:Good evening,

I am fairly new to studying for the GMAT and I haven't paid any real attention to math since college algebra.... six years or so ago now. Anyhow, I came across a problem and explanation in the OG16 book which I would like to devise a strategy for and others like it:

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

A) $10,350
B) $10,395
C) $10,500
D) $11,500
E) $12,705

The correct answer is B.

The book gave the following strategy:

10,000(1.10)(1.05)(.90)=10,395

My question is, are there any fast strategies to deal with this rather than multiply these numbers out?

Thank you in advance.

-Patrick
Rather than deal with all the changes TOGETHER (i.e., 10,000(1.10)(1.05)(.90)), it's easier to deal with increases and decreases of 5% and 10%, since these percentages are easy to calculate in our heads.

Here's a free video that explains how to do so: https://www.gmatprepnow.com/module/gmat ... video/1076

Cheers,
Brent
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by [email protected] » Wed Feb 17, 2016 8:22 pm
Hi pdonaldson1990,

Many GMAT Quant questions require 3-5 'steps' to get to the solution, so you shouldn't try to do all of the steps at once. Thankfully, the steps tend to be pretty easy to do, so you shouldn't rush through any of them and you should be sure to write everything on your pad (so that you can physically see the work).

Here, we're starting with $10,000. In the first year, the value increased by 10%....

Let's deal with THAT step right now:

10% of $10,000 = $1,000
New Total = $10,000 + $1,000 = $11,000

...increased by 5% during the second year....

Now we have $11,000, so the numbers will be a little different:

10% of $11,000 = $1,100
5% of $11,000 = $550
New Total = $11,000 + $550 = $11,550

...DECREASED by 10% during the third year...

10% of $11,550 = $1,155
New Total = $11,550 - $1,155 = $10,395

There's actually a great shortcut in this last calculation. If you look at the 'units digits' of the two numbers, you can deduce that when you subtract one from the other, you end up with a number that ends in 5... Take a good look at the answer choices; how many are LESS than $11,550 AND end in a 5?

Final Answer: B

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by GMATGuruNY » Thu Feb 18, 2016 3:45 am
pdonaldson1990 wrote: 10,000(1.10)(1.05)(.90)

My question is, are there any fast strategies to deal with this?
Use FRACTIONS instead of decimals, as follows:
(10,000)(110/100)(105/100)(90/100)

In the expression above, all of the 0's in red CANCEL OUT, leaving:
(1)(11)(105)(9)

= 99*105

= (100-1)(105)

= 10500 - 105

= 10395.
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by Matt@VeritasPrep » Thu Feb 18, 2016 6:10 pm
pdonaldson1990 wrote:
10,000(1.10)(1.05)(.90)
10,000 * (11/10) * (21/20) * (9/10) =

10,000/(10*20*10) * (11 * 21 * 9) =

5 * 11 * 21 * 9

The last step is still a bummer, but once you multiply those out you get the right answer.
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by Scott@TargetTestPrep » Wed Apr 04, 2018 4:56 pm

Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?

A) $10,350
B) $10,395
C) $10,500
D) $11,500
E) $12,705
To determine the value of the account today, we want to set up an expression showing the various percent increases and decreases.

Also, we must remember that a 10% increase is the same as multiplying by 1.1, a 5% increase is the same as multiplying by 1.05, and a 10% decrease is the same as multiplying by 0.9. That is:

10,000(1.1)(1.05)(0.9)

Because the multiplication may get a bit complicated in the equation above, we should convert each decimal to a fraction, allowing us to reduce before multiplying.
Thus, we have:

10,000(11/10)(105/100)(9/10)

This is equivalent to: 10,000(11 x 105 x 9/10,000)

Thus we see the the two values of 10,000 cancel out, and we are left with:

11 x 105 x 9 = 99 x 105 = 10,395

Note: If you did not want to perform the multiplication of the final step, you could have used a combination of units digits and estimation to come to the correct answer. Keep in mind that the product of 99 and 105 will have a units digit of 5. That leaves us with only B ($10,395) and E ($12,705) as possible answer choices. Next, by rounding up 99 to 100 and multiplying 100 by 105 we get a product of 10,500. Because we rounded up and answer choice E is LARGER than 10,500, it's not a possible answer choice. Thus, the correct answer is B, $10,395.

Answer: B

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