John places balls into 7 boxes, putting at least one ball in each box.

Question

John places balls into 7 boxes, putting at least one ball in each box. Did he place more than 7 balls in any one box?

(1) The number of balls in each of the 7 boxes is different.
(2) The total number of balls placed in the boxes is 29.

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John puts balls in 7 boxes, and put at least 1 ball in each box. Did he put more than 7 balls in at least one box?

1) The number of balls in each of the 7 boxes are different 
 2) The total number of balls put into box is 29.

ManifestDreamMBA · Answer

Did he place more than 7 balls in any one box?

Statement 1
Since there are at least one ball in each box. The min number of balls in each box could be as shown below
Boxes. 1--2--3 --4--5--6--7
Min Balls 1--2--3 --4--5--6--7
We cannot be sure that it is more than 7
Insufficient

Statement 2
T = 29
But we don't know anything else to answer the question
Boxes could have 4,4,4,4,4,4,5 or 1,1,1,1,1,1,23
Insufficient

Combined, we have If we consider scenario in statement 1, we have total = 7*6/2 = 21. This suggests at least 1 box has more than 7 balls

Answer C

GMATinsight · Answer

Boxes = 7
Keeping minimum one ball in 7 boxes requires minimum 7 balls

A great tip for hard questions like this:  to ensure that he has more than 7 balls in at least one box, balls required = 6*6 (6 balls in 6 boxes each) +7 (balls in 7th box) = 36+7 = 43

Question: Did he place more than 7 balls in any one box?

Statement 1  : The number of balls in each of the 7 boxes is different.

i.e. balls have to be minimum {1, 2, 3, 4, 5, 6,   7  }
so one box is certain to get min 7 balls hence
 SUFFICIENT

Statement 2  : The total number of balls placed in the boxes is 29.
that's not sufficient however if this number would have been 43 instead of 29 (as mentioned above in highlighted box area) then it could have been succificient
 NOT SUFFICIENT

Answer: Option A
 Fun problem Video:

https://www.youtube.com/watch?v=KU57y5ygCDI

Sketchitesh · Answer

7 boxes, at least 1 ball in each box.
Q: in any one box , is total balls >7 ?

S1: different balls in each box :
Case 1: 1,2,3,4,5,6,7 =>Is any one box ball > 7 (NO)  (note: Q says more than 7 not greater than equal to 7)

Case 2: 2,3,4,5,6,7,8 => Is any one box ball > 7 (YES)  Insufficient

S2: Total no of balls = 29

Case 1: 1,1,1,1,1,1,23 (YES)
Case 2: 4,4,4,4,4,4,5. (NO)  Insufficient

Combined, 1,2,3,4,5,6,7 = 28, for 29 at least one box must have >7 balls if all are different and at least 1 ball in each box.  SUFFICIENT

C is the answer

Missinga · Answer

John places balls into 7 boxes, putting at least one ball in each box. Did he place more than 7 balls in any one box?

(1) The number of balls in each of the 7 boxes is different.
Minimum number of balls in each box can be 1,2,3,4,5,6,7 or 2,3,4,5,6,7,8 or......
It is certain that minimum number of balls in a box can be equal to or more than 7. We need to find more than 7. 
Insufficient

(2) The total number of balls placed in the boxes is 29
The balls can be (4,4,4,4,4,4,5) or (7,6,4,4,3,2,1) or .....there are many possibilities 
Insufficient

(1)&(2) 
There are total 29 balls and each box has different number of balls in it. (1,2,3,4,5,6,8)

Answer: C

Dereno · Answer

There are seven boxes numbered B1, B2 ......... till B7.

Each boxes contain  ATLEAST  one ball.

To find   : If any one box has more than 7 balls ?.

Statement 1: 
  
(1) The number of balls in each of the 7 boxes is different.

so, the minimum ball a box can have is 1.

each boxes has different number of balls. Then, box 2, box 3,.... Box 7 has 2,3,4,5,6,7.

No box has more than 7 balls

Since, there is no upper limit on the number of balls or total ball count.

We can create another case, 1,3,5,7,9,11,13 . Here at least three boxes has balls > 7.

Hence,  Insufficient .

Statement 2: 
  
(2) The total number of balls placed in the boxes is 29.

29 balls are distributed among 7 boxes. One possible case is 4,4,4,4,4,4,5. So, no box has greater than 7 balls.

Another scenario is 2,2,6,8,9,1,1. Here two boxes has more than 7 balls.

insufficient

Combining statements 1 and 2, we get

Constraints : at least 1 ball per box 
stmt 1: each box has different number of balls. 
stmt 2: total balls to be distributed is 29.

Let the boxes be B1, B2, B3, B4, B5, B6, B7.

let’s first distribute one ball to each boxes. After distributing 7 balls, we are left with 22 balls.

leaving the first box, let’s give 1 ball to box 2. Count of B1 =1, B2 =2 
Then, give 2 balls to B3, we get B3 = 3 
three balls to B4, four balls to B5, five balls to B6, and 6 balls to B7

the distribution will be as follows

B1= 1
B2 = 1+1 =2
B3 =1+2 = 3
B4 = 1+3 =4
B5 = 1+4 = 5
B6 = 1+ 5 =6 
B7 = 1+ 6 = 7

adding all the balls, we get 28 and one ball remains. We can’t distribute the last ball to B1 thro B6, because giving any one to them will result in duplication. Statement 1 ( different numbered balls ) becomes compromised.

last ball is given to B7 will result in 8 balls. Thus one box has more than 7 balls .  Sufficient

Option C

sujoykrdatta · Answer

Condition: at least one ball in each box

S1: number of balls in each box is distinct. 
If we assume the least possible numbers, those would be: 1,2,3,4,5,6,7 - no box has more than 7 balls
Alternatively the distribution could also have been: 
1,2,3,4,5,6,8 - one box has more than 7 balls
Thus, insufficient

S2: Total balls is 29
One possible case: 1,1,1,1,1,1,23 - one box has more than 7 balls
Another case: 4,4,4,4,4,4,5 - no box has more than 7 balls
Thus, insufficient

Combining: 
Distinct number of balls in each box and a total of 29 balls: 
If we assume the least possible distinct number of balls in each box, those would be 1,2,3,4,5,6,7; this adds up to 28. However, we need 29 balls. The only way would be to have 1,2,3,4,5,6,8 (we cannot increase the numbers from 1 to 6 since that would result in one of the numbers to be repeated).

Thus, one box has more than 7 balls - Sufficient

Ans C

sujoykrdatta · Answer

For S1, the distribution doesn't have to be the minimum possible one. 1,2,3,4,5,6,8 is also possible

sujoykrdatta · Answer

The question is asking if there is more than 7 balls in a box, not if there is at least 7 balls in a box. So A isn't sufficient

John places balls into 7 boxes, putting at least one ball in each box.

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GMAT Data Sufficiency (DS) Questions

John places balls into 7 boxes, putting at least one ball in each box.

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