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The ratio of cupcakes to children at a particular birthday party is 10
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30 May 2021, 23:46
30 May 2021, 23:46
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Question Stats:
63% (02:40) correct
36% (03:12) wrong based on 58 sessions
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The ratio of cupcakes to children at a particular birthday party is 104 to 7. Each child at the birthday party eats exactly x cupcakes (where x is a positive integer) and the adults attending the birthday party do not eat anything. If the number of cupcakes that remain uneaten is less than the number of children at the birthday party, what must be true about the number of uneaten cupcakes?
I. It is a multiple of 2.
II. It is a multiple of 3.
III. It is a multiple of 7.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
I. It is a multiple of 2.
II. It is a multiple of 3.
III. It is a multiple of 7.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
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Joined: 11 Jan 2021
Posts: 29
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Re: The ratio of cupcakes to children at a particular birthday party is 10
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16 Jul 2021, 07:10
16 Jul 2021, 07:10
5
As void wrote,
assuming number of children at the party = 7, number of cupcakes = 104
Number of cupcakes eaten = 7x
Thus, \(104 - 7x < 7\)
Solving this, we get \(x > 13.857\)
As x is a positive integer, x = 14, 15, 16....
Now, Number of uneaten cupcakes \(= 104 - 7x\)
We see that x cannot be greater than 14 otherwise the number of uneaten cupcakes becomes negative.
Thus, uneaten cupcakes \(= 104 - 7*14 = 6\)
So, it is a multiple of 2 and 3. Option (D) is correct.
assuming number of children at the party = 7, number of cupcakes = 104
Number of cupcakes eaten = 7x
Thus, \(104 - 7x < 7\)
Solving this, we get \(x > 13.857\)
As x is a positive integer, x = 14, 15, 16....
Now, Number of uneaten cupcakes \(= 104 - 7x\)
We see that x cannot be greater than 14 otherwise the number of uneaten cupcakes becomes negative.
Thus, uneaten cupcakes \(= 104 - 7*14 = 6\)
So, it is a multiple of 2 and 3. Option (D) is correct.
General Discussion
Re: The ratio of cupcakes to children at a particular birthday party is 10
[#permalink]
02 Jun 2021, 09:02
02 Jun 2021, 09:02
1
assumed value no. of children= 7 and total no. of cookies 104 and x=total no. of cookies eaten by children.
second statement cannot be true if we take no. of cookies eaten by children is 70 then, no. of uneaten cookies is 104-70=34 which is multiple of 2 not 3.
second statement cannot be true if we take no. of cookies eaten by children is 70 then, no. of uneaten cookies is 104-70=34 which is multiple of 2 not 3.
