A retailer sells only radios and clocks...

[FabianB380]

Hello everybody,

i have a question concerning the following Data Sufficiency problem in the Algebra Strategy Guide (Problem set Chapter 9 p. 133):

A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

(1) The retailer has more than 28 radios in inventory
(2) The retailer has less than twice as many radios as clocks in inventory

The question asks for the radios in the inventory. so what is r in the equation? (r+c=44)


(1) INSUFFICIENT: This only tells you that r≥29 and r could be 29, 30, 40 etc.
(2) INSUFFICIENT: This only tells you that r<2c.

However, if you isolate c in the equation, you can substitute c in the inequality. => c=44-r

r<2c
r<2*(44-r)
r<88-2r
3r<88
r<88/3

Thus, 88/3 is equal to 29 1/3. Now i know that r must be less than or equal to 29 (because r must be an integer)

(1) and (2) are SUFFICIENT: Statement (1) tells you r≥29 and statement (2) tells you r≤29. Therefore r must equal 29.

The Algebra Strategy guide tells me that the correct answer is (C). And this means normally that the data either in statement (1) alone or in statement (2) alone are sufficient to answer the question.
I am confused does the solution not tell you that (1) and (2) together are necessary to answer the question? So the answer to this question would be (E), or am i wrong?

Can somebody help me with this problem?

I am deeply grateful for every explanation!!!!!!


Fabian

[tim]

You are confusing answer choices C and D. Go back and read the actual wording of the answer choices and you'll see it pretty quickly. And remember, it is of supreme importance that you remember exactly what these answer choices are and what each means.

BTW from your description it sounds overwhelmingly clear that you are not using the AD/BCE grid to solve these problems, because if you were the mere mechanics and location of the answer choices would have led you to C even without a second thought as to what it stood for. Be sure to use the grid for every problem so you can avoid problems like these.

[RonPurewal]

also, this is the wrong folder for your question.

there are two folders for MPrep materials: one for CAT problems, and one for all of our other materials.

going forward, please be sure to post your questions in the correct folder(s). thank you.