Liam has 3 times as many trading cards as Noah. Together they have 56 cards. How many cards does Noah have?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
QuantProblem Solving
Free GMAT Problem Solving Practice Question
PrepLattice is an independent test-preparation service and is not affiliated with or endorsed by GMAC, the organization that administers the GMAT. GMAT and GMAT Focus are trademarks of GMAC, used here only to name the exam this question is designed to prepare you for.
Answer & Explanation
Correct answer
A
Liam has 3 times as many cards as Noah, so Noah counts as 1 part and Liam as 3 parts, and the two of them hold 4 parts in all. Those 4 parts equal 56 cards, so one part is 56 ÷ 4 = 14, and Noah, who is the 1-part person, has 14 cards. That is choice (A). Check it: Liam's 42 + Noah's 14 = 56.
The most tempting wrong answer is (B) 18, which comes from dividing 56 by 3 because the stem says '3 times': 56 ÷ 3 leaves 18 with 2 cards left over, and keeping the whole-number part gives 18. But the 3 is a comparison between the two boys, not the number of shares to split the total into; there are 4 parts, not 3. Choice (D) 42 does the arithmetic correctly but reports Liam's cards instead of Noah's, so it answers for the wrong person. Choice (C) 28 splits the 56 evenly in half and ignores that Liam has 3 times as many, not the same amount. Choice (E) 56 simply hands back the combined total from the stem without solving for either boy.
Count the parts, divide the total by all of them, then answer for the person the question actually names: 14.