What is the number of 10 cents coins in the piggy bank?

Solution

Step 1: Analyse Question Stem

We need to find the number of 10 cents coin.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: A total of 69 coins are in three denominations of 25 cents, 50 cents, 10 cents, and 1 cent coins.

• The total number of coins = 69.

o We don’t know the breakup of these coins.
o Thus, we cannot find the number of 10 cents coins.

Hence, statement 1 is not sufficient, we can eliminate answer options A and D.

Statement 2: The number of 25 cents, 50 cents and 1, cents coins are in the ratio 18: 7: 12.

• Let 18x, 7x, and 12x be the number of 25 cents, 50 cents, and 1 cent coins, respectively.

o Total number of 25 cents, 50 cents, and 1 cent coins = 18x+7x+12x = 37x
o We cannot find the number of 10 cents coins with this information.

Hence, statement 2 is also not sufficient, we can eliminate answer options B.

Step 3: Analyse Statements by combining.

From statement 1: Total number of coins = 69
From statement 2: Total number of 25 cents, 50 cents, and 1 cent coin = 37x.
Note: - Many students will mark the answer as Option E because explicitly no information is given about 10 cent coins. Let’s see what’s the correct answer.

• 37x must be less than or equal to 69.

o 37x ≤ 69
o x ≤ 1.86

 We also know that x must be a positive integer.
 The only possible value of x is 1
• Total number of 25 cents, 50 cents, and 1 cents coin = 37*1 = 37

o Total number of 10 cent coin = 69 – 37 = 32.

Hence, the correct answer is Option C.
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OA is C
Statement 1: There are 69 coins. But we don't know the ratio of coins in which it is present (not sufficient)
Statement 2: 25, 50 and 1 cent coins are in the ration of 18:7:12. We don't know the maximum amount of coins in jar (not sufficient)

Combining both 25,50,1 cents are total in no. Of 37 which is less than 69 so the 10 cents coins will be 69-37 which is 32.
both statements are needed.
So OA is C

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What is the number of 10 cents coins in the piggy bank?

(1) A total of 69 coins are there in the denomination of 25 cents, 50 cents, 10 cents and 1 cent coins.
Since only total number of coins is given, the total amount can vary according to the number of 25 cents, 50 cents, 10 cents and 1 cent coins.
Case 1: 10 coins - 25 cents, 20 coins - 50 cents, 30 coins - 10 cents and 9 coins - 1 cent
Case 2: 20 coins - 25 cents, 20 coins - 50 cents, 20 coins - 10 cents and 9 coins - 1 cent

INSUFFICIENT.

(2) The number of 25 cents, 50 cents and 1 cents coins are in the ratio 18 : 7 : 12.
Total number of coins is not available so it can take any value.

INSUFFICIENT.

Together 1 and 2.
Let ratio of 25 cents, 50 cents and 1 cents coins = 18 : 7 : 12.
Then 18x + 7x + 12x + n(10) = 69 where x > 0 (integer since coins can take only integer value)
37x + n(10) = 69
x ≠ 2 because 37*2 = 74 which is not possible

Hence x = 1
Therefore n(10) = 69 - 37*1 = 32

SUFFICIENT.

Answer C.
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What is the number of 10 cents coins in the piggy bank?

(1) A total of 69 coins are there in the denomination of 25 cents, 50 cents, 10 cents and 1 cent coins.
(2) The number of 25 cents, 50 cents and 1 cents coins are in the ratio 18 : 7 : 12.

1) So, there are 69 coins in the bank which consists of 25 cents, 50 cents, 10 cents and 1 cent. A number of possibilities can happen like there may be 60 coins of 1 cent, 5 coins of 10 cent and among the remaining 4, 2 are from each of the other two denomination or any other combination can be drawn. Clearly, not sufficient.

2) We are given the ratio of the coins with other denomination beside the 10 cent coin. So not sufficient.

Together, Total coin = 69. Ratio of 25 : 50 : 1 = 18x : 7x : 12x (total is 37x, where x is an integer). Since, the total is 69, if we take the value of x more than 1, it will exceed total number of coins. So, there is actually (67-37)= 30 coins of 10 cent denomination. Sufficient.

C is the answer.

(1) insufic

(2) insufic

(1/2) sufic
50cents=a
25cents=b
10cents=c
1cent=d

69=a+b+c+d
a+b+d=18x+7x+12x=37x
x=integer≥1
if x=2, 37(2)=74>69coins, thus x=1
a+b+d=37(1)=37
69-37=c

Ans (C)

(1) N-25c + N-50c + N-1c + N-10c = 69
We don't know the proportion of each denomination
NOT SUFFICIENT

(2) N-25c : N-50c : N-1c = 18 : 7 : 12.
We don't know the ratio of 10 cents to the other denominations.
NOT SUFFICIENT

(1)+(2) N-25c + N-50c + N-1c + N-10c = 69
If N-25c + N-50c + N-1c = 18 + 7 + 12 = 37 coins, then N-10 cents is 69-37 = 32 coins
Any other combination is unlikely because of the given ratio in (2) and number of coins must be a positive integer.
SUFFICIENT

FINAL ANSWER IS (C)

(1) A total of 69 coins are there in the denomination of 25 cents, 50 cents, 10 cents and 1 cent coins..........clearly insufficient
(2) The number of 25 cents, 50 cents and 1 cents coins are in the ratio 18 : 7 : 12......without knowing total no.of coins we cannot find no.of 10 cent coins...,....insufficient

combing both we can get......no.of 10 cent coins=69-(18+7+12) =32

OA:C

What is the number of 10 cents coins in the piggy bank?

(Statement1): A total of 69 coins are there in the denomination of 25 cents, 50 cents, 10 cents and 1 cent coins.
—> No info about the ratio of these coins.
Insufficient.

(Statement2) : The number of 25 cents, 50 cents and 1 cents coins are in the ratio 18 : 7 : 12.
—> No info about the total number of coins. Also, the ratio of the number of 10 cents to that of other coins is not given.
Insufficient

Taken together 1&2,
—> In total, there are 69 coins.

The number of 25 cents, 50 cents and 1 cents should be 18+7+12 = 37 ( otherwise, 2(18+7+12) =74 >69)

69–37 = 32 —the number of 10 cents
Sufficient

The answer is C

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I feel E should be the answer as value of ratio for 10 cent coins isn't provided.

What is the number of 10 cents coins in the piggy bank?

(1) A total of 69 coins are there in the denomination of 25 cents, 50 cents, 10 cents and 1 cent coins.
(2) The number of 25 cents, 50 cents and 1 cents coins are in the ratio 18 : 7 : 12.
Solution:
Let, the number of 25 cents coin, 50 cents coin, 10 cents coin and 1 cent coin be a, b, c and d respectively.
From statement (1),
a + b + c+ d = 69, Clearly Not Sufficient.

From statement (2),
There is no mention of the number of 10 cents coin. Hence, Not Sufficient.

Combining both statements, As ratio is not actual figure, Not sufficient.

Answer: E