A box contains a certain number of cards, each of which is labeled by

Question

A box contains a certain number of cards, each of which is labeled by one of the values 4, 8, or 10. The numbers of cards labeled by each value are directly proportional to the values on the cards. What is the least possible number of cards in the box labeled by the value 10?

A. 5

B. 10

C. 11

D. 20

E. 22

A. 5

B. 10

C. 11

D. 20

E. 22

MartyTargetTestPrep · Answer

It's temping to pick 10, but the fact that 10 seems obviously correct is a clue indicating that we should look more carefully to see whether the only choice smaller than 10, which is 5, can somehow work.

rajtare · Answer

no. of cards with value 4 = 4x
no. of cards with value 8 = 8y
no. of cards with value 10 = 10z

10z will have the least integer value (as cards cant be in fractions) when z=1/2 hence the correct answer should be A.

JoeKan1234 · Answer

Since the numbers of cards labeled by each value are directly proportional to the values ​​on the cards, let k be the constant.

Let no. of cards with value 4 = 4k
Let no. of cards with value 8 = 8k
Let no. of cards with value 10 = 10k

HCF (4, 8, 10) = 2

So the value of k for 4k, 8k and 10k to be minimum positive integers is 1/2

Min. value of 10k = 10*0.5=5

Regor60 · Answer

The question needs to be rewritten.

The nearest antecedent to "each of which" is "cards", indicating that the cards themselves are numbered and that a box contains a mixture of such cards.

The last sentence refers to a box being numbered, which is not consistent with the above.

Posted from my mobile device

mx39 · Answer

If we're talking about direct proportionality, it is  much  easier to express this question in terms of a ratio. Really what this question is saying is, "if cards a, b, and c are in a box in a ratio of 4:8:10, what is the last number of card c?" In this case, divide the proportion by 2 and you get 2:4:5.

A box contains a certain number of cards, each of which is labeled by

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A box contains a certain number of cards, each of which is labeled by

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards