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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 11 May 2020, 04:18
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B
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95% (hard)

Question Stats:

46% (02:31) correct 54% (02:37) wrong based on 123 sessions

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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. He needs to buy a present but he doesn't know the price. What he knows is that the price is an integer from $1 to $100(both inclusive). What is the least number of coins he must bring so that he can buy the present without a change?

A. 11
B. 13
C. 15
D. 17
E. 19
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B
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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 11 May 2020, 04:27
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1x1
2x2
5x1
10x9

(b) 13
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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 11 May 2020, 04:31
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The number of coins needed to cover cost from 1 to 10:
1:1
2:2
5:1
Minimum number of coins needed to cover cost from 10 to 100:
10:9
With the above coins we can make any number within 1-100
Total coins needed are 13

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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 12 May 2020, 19:46
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ArunSharma12
The number of coins needed to cover cost from 1 to 10:
1:1
2:2
5:1
Minimum number of coins needed to cover cost from 10 to 100:
10:9
With the above coins we can make any number within 1-100
Total coins needed are 13

Posted from my mobile device
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Hi, thank you for the result!

How did you arrived to this answer? I'm asking so in case a similar question appears I can follow the same method/way to approach the question
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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 12 May 2020, 23:34
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jcerdae

To buy the gift of cost $1, $2, $3 and $4, John must have either 1 $1 coin and 2 $2 coins or 2 $1 coins and 1 $2 coins. First choice is better because if taken all together, it will sum up to 5 which can be used to decrease the number of $5 coins by 1.

Now we see that if we are able to sum up to any multiple of 5, then we can get any integer using 1 $1 coin and 2 $2 coins. Now we don't need any more $1 coin and $2 coins.

Now we have to get multiple of 5 using $10 coins and $5 coins. Obviously these coins will give multiple of 5 but these coins should as much to get sum of 95. To get least number of coins, we have to maximize number of $10 coins.

95 = 9 $10 coins + 1 $5 coin. This combination has least number of coins. Hence John must have 1 $1 coin, 2 $2 coins, 1 $5 coin and 9 $10 coins with a total of 13 coins.
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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 12 May 2020, 23:35
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jcerdae
ArunSharma12
The number of coins needed to cover cost from 1 to 10:
1:1
2:2
5:1
Minimum number of coins needed to cover cost from 10 to 100:
10:9
With the above coins we can make any number within 1-100
Total coins needed are 13

Posted from my mobile device


Hi, thank you for the result!

How did you arrived to this answer? I'm asking so in case a similar question appears I can follow the same method/way to approach the question
Show more

hi,
In this question, important bits to note are
    price is an integer from $1 to $100(both inclusive).
    least number of coins get to the price without a change
Here price is not fixed so which ever coins you choose should be able to get to a price ranging from 1 to 100.
another version of this question where you have to use a similar logic, you'll see that in this question price is fixed and you'll have to figure out different ways to reach to that price: https://gmatclub.com/forum/the-united-states-mint-produces-coins-in-1-cent-5-cent-10-cent-25-c-322412.html#p2506954
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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 13 May 2020, 00:31
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Since we need to minimize the number of coins and still ensure that we can pay any $ amount, we need to ensure that the single digit values are taken care of AND the number of $10 coins are maximum.

We would definitely need 1 coin each of $1 and $2. If we have these, we can pay 3 amounts i.e. 1, 2 and 3.

But, to pay 4, we can have 1 more coin of $2. With these, we can pay any amount from 1 to 5 but we need a $5 coin to pay for amounts from 6 to 10.

By now, we have 1 coin of $1, 2 coins of $2 and 1 coin of $5 using which we can pay any amounts from 1 to 10. We have a total of 4 coins by now.

Beyond this stage, we just need $10 coins to pay any amount between 10 and 100. Since we already have $10 worth of coins with us, we need another 9 coins of $10.
Therefore, total number of coins = 1 + 2 + 1 + 9 = 13.

The correct answer option is B.

Hope that helps!
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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 13 May 2020, 19:55
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Thank you so much for the explanations!! They helped me to understand the approach!!
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John only has 100 $1 coins, 50 $2 coins, 20 $5 coins and 10 $10 coins. 22 Feb 2025, 07:11
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