Please Explain

[govind_raj_76]

There were 5 rats in 5 cages and each of the rats had 1 of 5 identical biscuits. Each of the rats ate some portion of its respective biscuit. How many rats ate more than half of the biscuits ?

1) The quantities eaten bt the five rats were in the ratio 1: 2 : 3: 4: 5

2) The total quantity of biscuits remaining was equivalent to two whole biscuits

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

[Stuart@KaplanGMAT]

There were 5 rats in 5 cages and each of the rats had 1 of 5 identical biscuits. Each of the rats ate some portion of its respective biscuit. How many rats ate more than half of its biscuit?

1) The quantities eaten by the five rats were in the ratio 1: 2 : 3: 4: 5

2) The total quantity of biscuits remaining was equivalent to two whole biscuits

(Changed the wording of the question so it makes sense.)

1) the rats could have eaten 10%, 20%, 30%, 40% and 50%, giving us an answer of 0/5.

The rats could have eaten 15%, 30%, 45%, 60%, 75%, giving us an answer of 2/5.

More than one answer, insufficient: eliminate A and D.

2) 2 biscuits left, so the rats collectively ate 3 biscuits.

Well, 3 could have eaten 90% and 2 15%, giving us an answer of 3/5.

Alternatively, all 5 could have eaten 60%, giving us an answer of 5/5.

More than one answer, insufficient: eliminate B.

Combined:

from (1), we know that there are 15 parts in the ratio; from 2, we know that the sum of all 15 parts is 3.

So, we could find the value of 1 part. Once we know the value of 1 part, we can calculate exactly how much each rat ate. If we know the exact amounts, we can certainly answer the question. Together sufficient, choose C!

[kstv]

1) Ratio of quantity eaten by each rat = 1/x : 2/x : 3/x : 4/x : 5/x
15/x = ? Insuff
2) 2 biscuits remain , but ratio of consumption is not known
Insuff
Combining 15/x = 5-2
IMO C

x = 5, Rats who ate more than half = 3