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Tom found a box of 220 baseball cards. Being a thoughtful older brothe

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Bunuel
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Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   11 Apr 2016, 04:06
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Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?

A. 110
B. 112
C. 116
D. 118
E. 120
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B
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chetan2u
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Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   13 Apr 2016, 20:59
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OptimusPrepJanielle wrote:
Bunuel wrote:
Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?

A. 110
B. 112
C. 116
D. 118
E. 120


This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/4)*(x/2) is an integer
Or x/8 is an integer.

Hence we need the lowest multiple of 8 from the given options.
Let us start from the lowest value:

Option A: 110. This is not a multiple of 8
Option B: 112 = 8*14. This is a multiple of 8. Hence the correct answer.
Correct Option: B


Hi,
Two points on your solution...
1) Our choice should be a multiple of 4 and not 8..
In your solution you have taken x as the overall number so TOTAL should be a multiple of 8 and 50% of it should be multiple of 4..
Quote:
This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/4)*(x/2) is an integer
Or x/8 is an integer.

Hence we need the lowest multiple of 8 from the given options.

Example-
total is 216..
ans will be 108, which is NOT a multiple of 8..

2) I am sure you meant it, but did not write..
Before checking for multiples in choices, we should eliminate any choice which is less than 110, Luckily we do not have any such case..
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Re: Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   11 Apr 2016, 08:42
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Bunuel wrote:
Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?

A. 110
B. 112
C. 116
D. 118
E. 120


This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/4)*(x/2) is an integer
Or x/8 is an integer.

Hence we need the lowest multiple of 8 from the given options.
Let us start from the lowest value:

Option A: 110. This is not a multiple of 8
Option B: 112 = 8*14. This is a multiple of 8. Hence the correct answer.
Correct Option: B
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Re: Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   13 Apr 2016, 19:54
Bunuel wrote:
Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?

A. 110
B. 112
C. 116
D. 118
E. 120


220/2 = 110 however does not go into 4

112 goes into 4 --> We can stop here as 112 is the smallest number above 110 that goes into 4 (not need to divide you can use the divisibility rule)
If you want to check
220-112 = 108

108/4 = 27... for each brother
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OptimusPrepJanielle
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Re: Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   13 Apr 2016, 23:16
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Hi chetan2u,

Thanks a lot for pointing out :)
Since there are no options below 110, so there is no point even thinking about values less than 110
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chetan2u
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Re: Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   13 Apr 2016, 23:27
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OptimusPrepJanielle wrote:
Hi chetan2u,

Thanks a lot for pointing out :)
Since there are no options below 110, so there is no point even thinking about values less than 110


Hi OptimusPrepJanielle,

Firstly, your post is a reason for me to have respect for you. I am pretty sure the BEST of the GMAT instructors including you can overlook certain aspects in a hurry, BUT MOST of them do not get back to that topic OR give feeble defense for something indefensible, when pointed out.

Regards
Chetan
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Re: Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   13 Apr 2016, 23:46
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chetan2u wrote:
OptimusPrepJanielle wrote:
Hi chetan2u,

Thanks a lot for pointing out :)
Since there are no options below 110, so there is no point even thinking about values less than 110


Hi OptimusPrepJanielle,

Firstly, your post is a reason for me to have respect for you. I am pretty sure the BEST of the GMAT instructors including you can overlook certain aspects in a hurry, BUT MOST of them do not get back to that topic OR give feeble defense for something indefensible, when pointed out.

Regards
Chetan


Thanks a lot Chetan for the kind words.
We are all here to learn, make mistakes and keep on improving ourselves.

Cheers!
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Re: Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink] New post   06 Sep 2021, 02:19
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Re: Tom found a box of 220 baseball cards. Being a thoughtful older brothe [#permalink]
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