## A craftsperson made 126 ornaments and put them all into

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### A craftsperson made 126 ornaments and put them all into

by BTGmoderatorDC » Thu May 02, 2019 12:42 am

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A craftsperson made 126 ornaments and put them all into boxes. If each box contained either 6 ornaments or 24 ornaments, how many of the boxes contained 24 ornaments?

(1) Fewer than 4 of the boxes contained 6 ornaments

(2) More than 3 of the boxes contained 24 ornaments

OA A

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by [email protected] » Thu May 02, 2019 2:10 am

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## Global Stats

BTGmoderatorDC wrote:A craftsperson made 126 ornaments and put them all into boxes. If each box contained either 6 ornaments or 24 ornaments, how many of the boxes contained 24 ornaments?

(1) Fewer than 4 of the boxes contained 6 ornaments

(2) More than 3 of the boxes contained 24 ornaments

OA A

Source: GMAT Prep
Say there are x numbers of boxes that contained 6 ornaments and y numbers of boxes that contained 24 ornaments; thus, we have

6x + 24y = 126
x + 4y = 21

y = (21 - x)/4

We have to get the value of y.

(1) Fewer than 4 of the boxes contained 6 ornaments.

=> x: { 1, 2, 3}

Since x and y are positive integers, values of y must be such that y = (21 - x)/4 is a positive integer.

@x = 1, we have y = (21 - x)/4 = (21 - 1)/4 = 5;
@x = 2, we have y = (21 - x)/4 = (21 - 2)/4 = not an integer, not valid;
@x = 3, we have y = (21 - x)/4 = (21 - 3)/4 = not an integer, not valid

Thus, y = 5. Sufficient.

(2) More than 3 of the boxes contained 24 ornaments.

=> y: {4, 5, 6, ...}

Let's manipulate y = (21 - x)/4 to x = 21 - 4y

@y = 4, we have x = 21 - 4y = 21 - 4*4 = 5;
@y = 5, we have x = 21 - 4y = 21 - 4*5 = 1

No unique value of y. Insufficient.

Hope this helps!

-Jay
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by [email protected] » Sun Nov 03, 2019 7:26 pm

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## Global Stats

BTGmoderatorDC wrote:A craftsperson made 126 ornaments and put them all into boxes. If each box contained either 6 ornaments or 24 ornaments, how many of the boxes contained 24 ornaments?

(1) Fewer than 4 of the boxes contained 6 ornaments

(2) More than 3 of the boxes contained 24 ornaments

OA A

Source: GMAT Prep
We can let a = the number of boxes containing 6 ornaments each and b = the number of boxes containing 24 ornaments each. We can create the equation:

6a + 24b = 126

6a = 126 - 24b

Dividing both sides of the equation by 6, we have: a = 21 - 4b

We see that the value of b could be 0, 1, 2, 3, 4 or 5, and the respective values of a would then be 21, 17, 13, 9, 5,and 1.

Statement One Only:

Fewer than 4 of the boxes contained 6 ornaments.

In other words, a < 4. From the stem analysis, we see that if a < 4, then a must be 1, and hence b must be 5. So the number of boxes that contain 24 ornaments is 5. Statement one alone is sufficient.

Statement Two Only:

More than 3 of the boxes contained 24 ornaments.

In other words, b > 3. From the stem analysis, we see that if b > 3, then b must be 4 or 5, and hence, a must be 9 or 1, respectively. In the former case, the number of boxes that contain 24 ornaments is 4; however, in the latter case, the same number is 5. Statement two alone is not sufficient.

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### Re: A craftsperson made 126 ornaments and put them all into

by [email protected] » Mon May 02, 2022 6:51 am

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## Global Stats

BTGmoderatorDC wrote:
Thu May 02, 2019 12:42 am
A craftsperson made 126 ornaments and put them all into boxes. If each box contained either 6 ornaments or 24 ornaments, how many of the boxes contained 24 ornaments?

(1) Fewer than 4 of the boxes contained 6 ornaments

(2) More than 3 of the boxes contained 24 ornaments

OA A

Source: GMAT Prep
Given: A craftsperson made 126 ornaments and put them all into boxes. Each box contained either 6 ornaments or 24 ornaments.
In situations like this, where there aren't many possible cases, I like to invest a little time upfront to systematically list those cases.
case i: 0 24-ornament boxes and 21 6-ornament boxes
case ii: 1 24-ornament boxes and 17 6-ornament boxes
case iii: 2 24-ornament boxes and 13 6-ornament boxes
case iv: 3 24-ornament boxes and 9 6-ornament boxes
case v: 4 24-ornament boxes and 5 6-ornament boxes
case vi: 5 24-ornament boxes and 1 6-ornament boxes
Aside: I'd typically list the six possible outcomes in table form, which would take less than 15 seconds.

Target question: How many of the boxes contained 24 ornaments?

Statement 1: Fewer than 4 of the boxes contained 6 ornaments
This statement rules out cases i to v, leaving only case vi, which means 5 boxes contained 24 ornaments.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: More than 3 of the boxes contained 24 ornaments
This statement rules out cases i to iv, leaving cases v and vi, which means EITHER 4 boxes contained 24 ornaments OR 5 boxes contained 24 ornaments.
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT