Test: Two Part Analysis - 1 - GMAT MCQ

The correct answers are 15 and 19. After two years, Customer 1’s $100 will have compounded at 10% four times: $110 after six months, $121 after one year, and $146.41 after two years.
The rate then changes to 5% annually, so after the third year that would be $146.41 * 1.05 = $153.73. And after the fourth year, Customer 1 would have $153.73 * 1.05 = $161.42.
“How much extra” Customer 1 earns is $161.42 − $146.41 = $15
If he moved to the Credit Union after two years, then that would be $146.41 compounded at 15% / 4 = 3.75% four times in the third year, and 6% /4 = 1.5% four times in the fourth year. You could use the formula for compounding interest as follows:

This second option would result in a final amount of $180.05, a difference of $18.63 (approximately $19) when compared with the earlier balance of $161.42.

The answer is 160 and 3. Customer 1 deposits $100 initially into the new account. If the amount P is invested at an annual interest rate of r percent, compounded n times per year, then the value V of the investment at the end of t years is given by the formula:

So after two years, the investment will be worth $146.41. That amount is then compounded annually for two more years at the adjusted rate of 5%. This formula becomes V = 146.41(1 + .05)². This becomes V = 161.42. Customer 1’s investment is worth approximately $161 after four years, which is closest to 160 in the table.
Customer 2 had an equal amount after two years, so he/she would also have $146.41. Then the interest is compounded quarterly for the next two years at 6%. The formula for this would look like:

That is a difference of 164.93 – 161.42 = 3.51, which is closest to 3.

The correct answers are 121 and 135. Customer 1 is placing $100 in Clearwater State Bank for one year only, so it will compound twice at 10%. Remember that 20% interest compounded semi-annually is the same as 10% interest compounded every six months. That will give the customer $100 x 1.1 = $110 after six months, and $110 x 1.1 = $121 after one year. Customer 1 then takes that $121 and places it in the Clearwater Credit Union for the remaining 9 months out of the 21 months total (12 months was the first year at the Clearwater State Bank). At Clearwater Credit Unit, the $121 will compound 4 times at 3.75% every quarter. After three months that will be $121 * 1.0375 = $125.54. After six months that will be $125.54 * 1.0375 = $130.25. After nine months that will be approximately $135.13, or $135.

The answer is 3 million and 10,000. This is a permutation question. The first thing we must find is the number of members on each team. 20 pairs total means we have 40 individuals. Team Legato has 1/4 as many members as Team Forte, so 1/4y + y = 40.
5/4y = 40
y = 32
Team Legato will have 8 members, and Team Forte will have 32 members.

We have three places, with six slots each, and we know that one team cannot “sweep,” and also that Team Legato must come in first place. The possible arrangements for team-placement are two:
Team L, Team F, Team L
Team L, Team L, Team F

Now we must consider how many ways we can order people within each placing team. In Outcome 1, we’d have 8 * 7 arrangements for Team Legato in first place, 32 * 31 arrangements for Team Forte in second place, and 6 *5 arrangements for Team Legato in third place.

8 * 7 * 32 * 31 * 6 * 5 = 1,666,560 possible placements for the individual team members. We must double this number to account for either possible team-placement, so the answer is approximately 3 million.

If there were half as many participants, there would be 20 individuals, so 16 on Team Forte and 4 on Team Legato. In Outcome 1, we’d have 4*3 for 1st place, 16*15 for 2nd place, and 2*1 for 3rd place. The possible arrangements would be 5760 for each outcome, or 11,520 total.

The answer is 1770 and 105. If there are 60 members on Forte, then there are 15 members of Legato. We’re choosing 2 from 60, and 2 from 15, so we’d need to use the Combination formula:
60! / (60-2)! 2! = 60 x 59 / 2 = 30 x 59 = 1770
15! / (15-2)! 2! = 15 x 14 / 2 = 15 x 7 = 105