Marbles are to be placed in 5 holes in a wall, so that no hole is left

Question

Marbles are to be placed in 5 holes in a wall, so that no hole is left unfilled and each hole contains at least as many marbles as any hole to the right of it. If the hole in the middle is to contain 3 marbles, what is the least total number of marbles required?

A. 5
B. 9
C. 10
D. 11
E. 15

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ManifestDreamMBA · Answer

Marbles are to be placed in  5 holes in a wall , 
so that  no hole is left unfilled  and 
 each hole contains at least as many marbles as any hole to the right of it.

_ _ 3 _ _

Min a hole can have is 1, so first 2 holes can both have 1 marble each and rest all can have 3 marbles

1   1   3   3   3

Total = 11

Dereno · Answer

Marbles are placed in five holes in a wall.

Let the holes be 🕳️ 🕳️ 🕳️ 🕳️ 🕳️

Minimum value without any constraint is 1 each = 1 1 1 1 1 = 5

With constraint hole in middle has 3 marbles.

Each hole contains at least as many marbles as any hole to the right of it.

If middle has 3, the other two hole to the right can contain 3 marbles each.

_ _ 3 3 3

The two hole in front of the middle one can contain 1 each.

1 1 3 3 3

Total 🟰 11

Option D

PunitJalan · Answer

The question stem states: Each hole contains at least as many marbles as any hole to the right of it --

Hence consider positions of marbles as P1, P2, P3, P4 and P5, therefore

Let's say that we want to know the minimum number of marbles in the first positions. This means we need to find the maximum number of marbles that are there in any position to the right of the first position. Hence, any number of marbles to the right of the first position will be less than or equal to the number of marbles at the first position.

This implies:

P1 >=  Max number of marbles out of (P2,P3,P4,P5)
and 
 P2 >=  Max number of marbles out of (P3,P4,P5) 
and
 P3 >=  Max number of marbles out of (P4,P5) 
and
 P4 >=  Number of marbles in P5

Hence

Marbles in positions P4 and P5 are less than or equal to the number of marbles in P3 but more than one (opposite of the third condition).

Hence, marble in P4 and P5 for the total number of marbles to be minimum is 1 because this always satisfies the third condition stated above, as 3>1.

The second condition states P2  >= 3 and for total number of marbles to be minimum P2 = 3

Similarly for Position 1: P1=3

Hence, the right order is:

3   3   3   1   1

Total : 11 (Answer: D)

Marbles are to be placed in 5 holes in a wall, so that no hole is left

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GMAT Problem Solving (PS) Questions

Marbles are to be placed in 5 holes in a wall, so that no hole is left

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