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24 Mar 2025, 00:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:42) correct
38%
(02:01)
wrong
based on 95
sessions
History
Date
Time
Result
Not Attempted Yet
A retailer sells only radios and clocks. If there are currently exactly 42 total items in inventory, how many of them are radios?
(1) The retailer has more than 26 radios in inventory.
(2) The retailer has less than twice as many radios as clocks in inventory.
(1) The retailer has more than 26 radios in inventory.
(2) The retailer has less than twice as many radios as clocks in inventory.
24 Mar 2025, 01:18
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- \(r\) be the number of radios.
- \(c\) be the number of clocks.
\(r + c = 42\)
Statement (1): \(r > 26\)
- This means \(c = 42 - r < 42 - 26 = 16\).
- So, \(r\) is between 27 and 42.
Not sufficient
Statement (2): \(r < 2c\)
- Substituting \(c = 42 - r\):
\(r < 2(42 - r)\)
\(r < 28\)
Not sufficient
Combining (1) and (2):
\(26 < r < 28\)
- This means \(r = 27\).
Sufficient - Option C
- \(c\) be the number of clocks.
\(r + c = 42\)
Statement (1): \(r > 26\)
- This means \(c = 42 - r < 42 - 26 = 16\).
- So, \(r\) is between 27 and 42.
Not sufficient
Statement (2): \(r < 2c\)
- Substituting \(c = 42 - r\):
\(r < 2(42 - r)\)
\(r < 28\)
Not sufficient
Combining (1) and (2):
\(26 < r < 28\)
- This means \(r = 27\).
Sufficient - Option C
24 Mar 2025, 06:49
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Bunuel
A retailer sells only radios and clocks. If there are currently exactly 42 total items in inventory, how many of them are radios?
(1) The retailer has more than 26 radios in inventory.
(2) The retailer has less than twice as many radios as clocks in inventory.
R + C = 42(1) The retailer has more than 26 radios in inventory.
(2) The retailer has less than twice as many radios as clocks in inventory.
Question: R = ?
Statement 1: R > 26
Value of R can be anything from 27 to 42 hence
NOT SUFFICIENT
Statement 2: R < 2C
Still we can't find unique value of R and C hence
NOT SUFFICIENT
Combining the statements
R > 26 and R < 2C
If R = 27 then C = 42-27 = 15 which makes R < 2C SATISFIED
If R = 28 then C = 42-28 = 14 which makes R = 2C i.e. R < 2c is NOT SATISFIED
i.e. we have a unique solution
R = 27 then C = 42-27 = 15
SUFFICIENT
Answer: Option C
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