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Herd of Cows

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by carlos.lara.7 » Thu Sep 15, 2016 4:13 pm
If a herd of cows is split in three unequal parts, how many there would be in the largest group?

(1) The number of cows in the two larger groups is 57. (2) The number of cows in the two smaller groups is 43.

A - statement (1), BY ITSELF is sufficient to answer the question but statement (2) by itself is not sufficient to answer the question

B - statement (2), BY ITSELF is sufficient to answer the question but statement (1) by itself is not sufficient to answer the question

C - BOTH statement (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement BY ITSELF is sufficient to answer the question

D - EACH statement BY ITSELF is sufficient to answer the question

E - the two statements, even when taken TOGETHER, are NOT sufficient to answer the question
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Source: — Data Sufficiency |

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by [email protected] » Thu Sep 15, 2016 4:41 pm
Hi carlos.lara.7,

We're told that a group of cows is split into 3 groups with a DIFFERENT number in each group. We're asked how many cows are in the LARGEST group.

1) The number of cows in the two larger groups is 57.

This Fact puts a limit on how big the largest group could be, but does NOT define the exact value of the group. For example...

IF...
Largest = 32
Middle = 25
Smallest = 18
Then the answer to the question is 32

IF...
Largest = 31
Middle = 26
Smallest = 17
Then the answer to the question is 31
Fact 1 is INSUFFICIENT

2) The number of cows in the two smaller groups is 43.

We face a similar situation in Fact 2 that we faced in Fact 1. This Fact tells us NOTHING about the size of the largest group though (only what it would be at the minimum).

IF...
Largest = 32
Middle = 25
Smallest = 18
Then the answer to the question is 32

IF...
Largest = 31
Middle = 26
Smallest = 17
Then the answer to the question is 31
Fact 2 is INSUFFICIENT

Combined, we still don't know the exact number of cows in any of the groups (the two examples that I provided 'overlap' with both Fact 1 and Fact 2), so there is clearly more than one possible answer.
Combined, INSUFFICIENT

Final Answer: E

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by Matt@VeritasPrep » Fri Sep 16, 2016 1:51 pm
Since the parts are unequal, let's call them a, b, c, with a > b > c.

S1:

a + b = 57

We could have anything: a = 41, b = 16, a = 53, b = 4, etc. Not sufficient.

S2:

b + c = 43

Same issue as above, not sufficient.

S1 + S2:

Three variables but only two equations! All we can say from the two together is that a - c = 14. (b could still be anything.) So we can't solve: we could have a = 33, b = 24, c = 19, or a = 32, b = 25, c = 18, etc. etc.
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