Nums99 wrote:
E-gmatRosy and Daisy bought some books, pens, and pencils. Out of the total amount spent by Rosy, what percentage account for the amount spent on buying pencils, if it is known that Daisy spends 1.5 times the amount spent by Rosy?
1) Rosy bought 4 books, 14 pens, and 10 pencils
2) Daisy bought 8 books, 28 pens, and 12 pencils
Clearly, each statement alone is insufficient, so you need to analyze both statements together.
You can set up equations using the statements and the fact that "Daisy spends 1.5 times the amount spent by Rosy".
>
Rosy: 4a + 14b + 10c = T
>
Daisy: 8a + 28b + 12c = 1.5T
Since the question is about pencils out of total, we need to isolate c and T. You can multiply the first equation by 2 and then subtract. This works because the coefficients of a and b in Rosy's equation are half of the coefficients in Daisy's -- that is the key fact in this problem.
> 8a + 28b + 20c = 2T
> 8a + 28b + 12c = 1.5T
----------------------
> 8c = 0.5T
That means that 16c = T, so Rosy's total is equal to 16 times the price of one pencil. Thus, Rosy's 10 pencils are 10/16 of the total.
Answer:
(c) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.