Problem Solving

BTGmoderatorLU wrote:Source: Manhattan Prep

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 OA is C.

Say there are x radios and y clocks.

Thus, we have x + y = 44.

We have to get the value of x.

Let's take each statement one by one.

1) The retailer has more than 28 radios in inventory.

x > 28. But we can't get the unique value of x. Insufficient.

2) The retailer has less than twice as many radios as clocks in inventory.

x < 2y. But we can't get the value of x. Insufficient.

(1) and (2) together

Given x > 28, x + y = 44 and x < 2y, we have

From x > 28 and x + y = 44, we have y < 16.
From x < 2y and x + y = 44, we have y > 14.66.

Thus, we have 14.66 < y < 16.

Since y is a positive integer, the only qualifying integer value for y is 15. Thus, x = 44 - 15 = 29.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Mehdipatnam | Hyderabad GMAT Prep | Bangalore GMAT Courses | Dilsukhnagar GRE Prep | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Hi All,

We're told that a retailer sells only radios and clocks and she currently has 44 total items in inventory. We're asked how many of those items are radios. This question can be solved by TESTing VALUES.

1) The retailer has MORE than 28 radios in inventory.

With 44 total items, and MORE than 28 radios, the number of radios could be any integer from 29 to 44, inclusive.
Fact 1 is INSUFFICIENT

2) The retailer has LESS than TWICE as many radios as clocks in inventory.

Just as in Fact 1, there are a number of different possibilities.
IF....
Radios = 28, Clocks = 16, then the answer to the question is 28
Radios = 27, Clocks = 17, then the answer to the question is 27
Fact 2 is INSUFFICIENT

Combined, we know...
-The retailer has MORE than 28 radios in inventory.
-The retailer has LESS than TWICE as many radios as clocks in inventory.

Fact 1 gives us a minimum number of radios, while Fact 2 gives us a maximum number of radios....
IF....
Radios = 29, Clocks = 15, then the answer to the question is 29
Radios = 30, Clocks = 14, then the number of radios is MORE than twice the number of clocks, so this option is NOT possible (and neither are any options that include more than 30 radios). Thus, there's only one possible outcome that fits everything we were told: 29 radios and 15 clocks.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote: ↑

Thu Nov 22, 2018 1:37 pm

Source: Manhattan Prep

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 OA is C.

Given: A retailer sells only radios and clocks, and she currently has 44 total items in inventory.

Target question: How many radios are there in the inventory

Statement 1: The retailer has more than 28 radios in inventory
There are several scenarios that satisfy statement 1. Here are three:
Case a: There are 29 radios and 15 clocks. In this case, the answer to the target question is there are 29 radios
Case b: There are 30 radios and 14 clocks. In this case, the answer to the target question is there are 30 radios
Case c: There are 31 radios and 13 clocks. In this case, the answer to the target question is there are 31 radios
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The retailer has less than twice as many radios as clocks in inventory.
There are several scenarios that satisfy statement 2. Here are three:
Case a: There are 29 radios and 15 clocks. In this case, the answer to the target question is there are 29 radios
Case b: There are 28 radios and 16 clocks. In this case, the answer to the target question is there are 28 radios
Case c: There are 27 radios and 17 clocks. In this case, the answer to the target question is there are 27 radios
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the number of radios can be 29, 30, 31, 32, . . . . 44
Statement 2 tells us that the number of radios can be 29, 28, 27, 26, . . . . 0
Since BOTH statements are true, the only scenario that satisfies BOTH statements is when there are 29 radios
So, the answer to the target question MUST be there are 29 radios
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent