Problem Solving

MalcolmW wrote: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

I really need a breakdown of this problem

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

Cheers,
Brent

Hi MalcolmW,

Breaking the question down into 'steps', and then doing the math 'one piece' at a time, is a great way to handle these types of questions (and Brent's approach is spot-on).

In the broad sense, we're dealing with percents, so we're just dealing with multiplication. For comparison purposes, you could also 'translate' the prompt into the following equation:

$10,000(1.1)(1.05)(0.9) = Value at the end of the third year

Looking at this, it's probably not going to be any easier to multiply the prompt out this way, so sticking with a step-by-step approach will serve you well (and it will help you on many other questions that you'll face during your studies and on Test Day).

GMAT assassins aren't born, they're made,
Rich

MalcolmW wrote: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 = $10,395

Answer: B

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

Cheers,
Brent

Hi All,

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

GMAT assassins aren't born, they're made,
Rich

MalcolmW wrote: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

I really need a breakdown of this problem

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 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 arrive at 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