One solution is to start TESTING answer choices.

A) 3
If there are 3 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 13 coins must be dimes (worth $0.10 each)
3 quarters = $0.75 and 13 dimes = $1.30
So the TOTAL value = 0.75 + $1.30 = $2.05
NO GOOD - we want a total of $2.35

B) 5
If there are 5 quarters (worth $0.25 each), and we have a total of 16 coins, the remaining 11 coins must be dimes (worth $0.10 each)
5 quarters = $1.25 and 11 dimes = $1.10
So the TOTAL value = 1.25 + $1.10 = $2.35
BINGO!

Answer:
_________________

Test confidently with gmatprepnow.com

25x + 10(16-x) = 235
15x = 75
x = 5

We can let the number of 10-cent coins = d and the number of 25-cent coins = q. We are given that there are 16 total coins; thus, d + q = 16.

We are also given that the total face value is $2.35, thus:

0.1d + 0.25q = 2.35

10d + 25q = 235

Isolating d in our first equation, we have d = 16 - q. We can substitute 16 - q for d in our second equation and we have:

10(16 - q) + 25q = 235

160 - 10q + 25q = 235

15q = 75

q = 5

There are 5 coins with a face value of 25 cents.

Answer: B
_________________

let x be 10 cents coin and y be 25 cents coin
then
10x+25y = 235.................(i)
x+y = 16 .................(ii)

(ii) * 10
10x+10Y = 160 ............(iii)

then (i) - (iii)
15 y = 75
y=5
Hence Answer B
_________________

Regards,
Naveen
email: nkmungila@gmail.com
Please press kudos if you like this post

Hi adkikani

in your assumption x represents 10 cents or 0.1 dollars, so total contribution from x coins will be 0.1x

similarly y represents 25 cents or 0.25 dollars, so total contribution from y coins=0.25y

Hence total amount =0.1x+0.25y=2.35

and total number of coins =16 i.e x+y=16

We know x + y = 16 ----- I

x = 16 - y -----(II)

Now, 0.10x + 0.25y = 2.35

0.10(16 - y) + 0.25y = 2.35

1.6 - 0.10y +0.25y = 2.35

1.6 - 0.15y = 2.35

y = 5

(B)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

For most word problems, you should at least consider the possibility of testing the answer choices. HOWEVER this doesn't necessarily mean that testing the answer choices will be the best/fastest approach.

I'd say that, in most cases, testing the answer choices is not the best approach. That said, it's a great strategy if you can't think of any other ways to solve the question.

In other situations, testing the answer choices is impossible. For example:

In how many ways can we arrange the letters in the word FAST?
A) 4
B) 8
C) 12
D) 16
E) 24

As you can see, there is no way to actually test the answer choices for this question.

I hope that helps.

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com