At a print shop, the manager recorded the number of flyers produced by

Question

At a print shop, the manager recorded the number of flyers produced by each of 10 copy machines during one shift. What was the standard deviation of the numbers of flyers produced by the 10 copy machines?

(1) Each of the 10 copy machines produced either 40 or 60 flyers.

(2) Exactly 6 of the 10 copy machines produced the same number of flyers.

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a print shop, the manager recorded the number of flyers produced by each of 10 copy machines during one shift. What was the standard deviation of the numbers of flyers produced by the 10 copy machines?

(1) Each copy machine produced either 40 or 60 flyers.

This gives the only possible values, but not how many machines produced each number.

Not sufficient.

(2) Exactly 6 of the 10 copy machines produced the same number of flyers.

This tells us only that 6 values are equal, but it does not tell us what those values are or what the other 4 values are.

Not sufficient.

(1)+(2) From statement (1), every value is either 40 or 60.

From statement (2), exactly 6 of the 10 values are the same.

So the distribution must be either:

6 machines produced 40 flyers and 4 machines produced 60 flyers: {40, 40, 40, 40, 40, 40, 60, 60, 60, 60}

or

6 machines produced 60 flyers and 4 machines produced 40 flyers: {40, 40, 40, 40, 60, 60, 60, 60, 60, 60}

These two distributions have the same standard deviation, because the same two values occur with the same frequencies, only which value occurs 6 times is switched.

Alternatively, we can check the distances from the mean.

The mean of the first set, {40, 40, 40, 40, 40, 40, 60, 60, 60, 60}, is:

(6 * 40 + 4 * 60)/10 = 48

So six values are 8 away from the mean, and four values are 12 away from the mean.

The mean of the second set, {40, 40, 40, 40, 60, 60, 60, 60, 60, 60}, is:

(6 * 60 + 4 * 40)/10 = 52

So again, six values are 8 away from the mean, and four values are 12 away from the mean.

Therefore, the standard deviation is the same in either case.

Sufficient.

Answer: C.

randomname4 · Answer

Statement (1)

Each machine produced either 40 or 60 flyers.

But we don’t know how many produced 40 and how many produced 60.

Examples:

5 machines made 40, 5 made 60
9 machines made 40, 1 made 60

Both satisfy statement (1), but they have different spreads.

So statement (1) alone is not sufficient.

Statement (2)

Exactly 6 of the 10 machines produced the same number of flyers.

But we don’t know what those numbers were.

Example:

Six machines made 40 flyers, others made different values
Six machines made 100 flyers, others made different values

Different possible spreads.

So statement (2) alone is not sufficient.

Together

From statement (1), every value is either:

40 or 60

From statement (2), exactly 6 machines produced the same number.

So the distribution must be either:

6 machines made 40,4 machines made 60

or

6 machines made 60,4 machines made 40

Either way, the spread is the same because the values are still split 6 and 4 between 40 and 60.

So we can determine the standard deviation.

Answer: C — both statements together are sufficient, but neither alone is sufficient.

vasu1104 · Answer

total machine = 10

find SD of flyers produced by these 10 machine.

need: mean and how far the num are spread from the mean.

S-1

each machine either produced 40 or 60.
three options might have happened here.
either all produced 40. SD = 0
each produced 60. SD = 0
or few produced 40 and rest 60. in that SD wont be zero.

so we have two different answers.
so not sufficient.

S-2

6 produced the same number of flyers.
but we don't know what that number is. also we don't know what's number of flyers produced by other 4 machines.

so this doesnt tell much.
 not sufficient.

S 1 & 2

either 40 or 60. and 6 produced same num.

in such case,
6 can have 40 and 4 can have 60
or, 4 can have 40 and 6 can have 60.

here mean will be different for both but spread would be in the same range.
so regardless of which case happened, the SD will be same in both case.

so this combined option is sufficient.

Option C

At a print shop, the manager recorded the number of flyers produced by

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At a print shop, the manager recorded the number of flyers produced by

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