A certain purse contains 30 coins, Each coin is either a...

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A certain purse contains 30 coins, Each coin is either a...

by BTGmoderatorLU » Fri Dec 15, 2017 1:47 pm

A certain purse contains 30 coins, each coin is either a nickel or a quarter. If the total value of all coins in the purse is $ 4.70, how many nickels does the purse contain?

A. 12
B. 14
C. 16
D. 20
E. 22

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

Quote

Source: Beat The GMAT — Problem Solving | Fri Dec 15, 2017 1:47 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri Dec 15, 2017 3:30 pm

LUANDATO wrote:A certain purse contains 30 coins, each coin is either a nickel or a quarter. If the total value of all coins in the purse is $ 4.70, how many nickels does the purse contain?

A. 12
B. 14
C. 16
D. 20
E. 22

The OA is B.

ASIDE: Each nickel is worth 5 cents ($0.05) and each quarter is worth 25 cents ($0.25)

Let n = the number of nickels in the purse
This means (30-n) = the number of quarters in the purse (since there is a total of 30 COINS)

Since each nickel is worth 5 cents, we know that n nickels is worth 5n CENTS
Likewise, since each quarter is worth 25 cents, we know that (30-n) quarters is worth 25(30-n) CENTS

The total value of all coins in the purse is $ 4.70
We can also say that the TOTAL value is 470 CENTS
So, we can write: (value of all nickels) + (value of all quarters) = 470 CENTS
Or: 5n + 25(30-n) = 470
Expand: 5n + 750 - 25n = 470
Simplify: -20n + 750 = 470
Subtract 750 from both sides: -20n = -280
Solve: n = 14

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Fri Dec 15, 2017 3:33 pm

Hi LUANDATO,

We're told that a purse contains 30 coins, each coin is either a nickel (worth $0.05 each) or a quarter (worth $0.25 each) and the total value of all coins in the purse is $4.70. We're asked for the number of nickels in the purse. This question can be solved in a couple of different ways (including a 'system' of Algebraic equations). However, there is a great 'shortcut' in this question that can help you avoid a lot of that 'math' and focus on the answer choices.

The total value of the QUARTERS in the purchase can only "end" in a few possibilities: .00, .25, .50 or .75. Since the total of ALL the coins is $4.70, the 20 cents above $4.50 can ONLY be from the value of 4 nickels. Thus, the number of nickels is going to be 4 greater than some 'round number' (meaning a multiple of 5 or 10). Let's TEST Answer B...

IF... there are 14 nickels....
14 nickels --> (14)($.05) = $0.70
30 total coins means 16 quarters --> (16)($0.25) = $4.00
$0.70 + $4.00 = $4.70
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: B

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

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Sep 23, 2019 4:37 pm

BTGmoderatorLU wrote:A certain purse contains 30 coins, each coin is either a nickel or a quarter. If the total value of all coins in the purse is $ 4.70, how many nickels does the purse contain?

A. 12
B. 14
C. 16
D. 20
E. 22

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

We can create the equations:

25q + 5n = 470

5q + n = 94

and

n + q = 30

q = 30 - n

Substituting, we have:

5(30 - n) + n = 94

150 - 5n + n = 94

56 = 4n

14 = n

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]