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Tom found a box of 220 baseball cards. Begin a thoughtful...

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Tom found a box of 220 baseball cards. Begin a thoughtful...

by BTGmoderatorLU » Sat Feb 10, 2018 7:38 am
Tom found a box of 220 baseball cards. Begin 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

The OA is B.

I'm confused by this PS question. Experts, any suggestion? Thanks in advance.
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by EconomistGMATTutor » Sat Feb 10, 2018 10:47 am
Tom found a box of 220 baseball cards. Begin 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

The OA is B.

I'm confused by this PS question. Experts, any suggestion? Thanks in advance.
Hi LUANDATO,
Let's take a look at your question.

Tom had a total of 220 baseball cards.
He wanted to save at least 50 percent of the cards for himself.
$$50\%\ of\ \ 220\ card=\left(\frac{50}{100}\right)\times220=110$$
Lets see if the remaining 110 cards can be distributed evenly among his 4 younger brothers.
$$\frac{110}{4}=27remainder2$$
It means if we distribute remaining 110 card evenly among 4 brothers, each of them will get 27 cards and 2 will be left.

Therefore, Tom will get 110 + 2 = 112 cards.

Hence option B is correct.

I am available if you'd like any follow up.
GMAT Prep From The Economist
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by [email protected] » Sat Feb 10, 2018 11:01 am
Hi LUANDATO,

We're told that Tom found a box of 220 baseball cards, he wanted to save AT LEAST 50 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers so that they would each have the SAME number of cards. We're asked for the LOWEST possible number of cards that Tom can save for himself under these conditions. This question can be solved with some Number Properties and TESTing THE ANSWERS.

Since Tom has 4 brothers, the total number of cards that he gives to them MUST be a multiple of 4. Thus, we're looking for the LEAST answer that is AT LEAST half of 220 and leaves us with a remaining number of cards that is a multiple of 4. We can use the 'rule of 4' to quickly determine which number that is.

The 'rule of 4': a number is divisible by 4 if the last 2 digits from a number that is divisible by 4.
For example....
132 is divisible by 4 because '32' is divisible by 4
10,525 is NOT divisible by 4 because '25' is NOT divisible by 4.

We're asked for the LEAST number of cards that Tom can keep for himself, so let's start with Answer A:

Answer A = 110 cards
If Tom keeps 110 cards for himself, that leaves 220 - 110 = 110 cards for his 4 brothers.
However, 110 is NOT divisible by 4 (because '10' is NOT divisible by 4), so this CANNOT be the answer.

Answer B = 112 cards
If Tom keeps 112 cards for himself, that leaves 220 - 112 = 108 cards for his 4 brothers.
However, 108 IS divisible by 4 (because '08' IS divisible by 4), so this MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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