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22 Jan 2025, 01:30
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Difficulty:
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57%
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At a used car lot, the number of blue cars was between 50 and 60. How many cars were at the lot in total?
(1) \(\frac{7}{15}\) of the cars at the lot were blue.
(2) The ratio of the number of blue cars to the number of red cars was 14 to 5.
(1) \(\frac{7}{15}\) of the cars at the lot were blue.
(2) The ratio of the number of blue cars to the number of red cars was 14 to 5.
Updated on: 22 Jan 2025, 03:31
Originally posted by bhargavhhhhhhhh on 22 Jan 2025, 03:06.
Last edited by bhargavhhhhhhhh on 22 Jan 2025, 03:31, edited 1 time in total.
Last edited by bhargavhhhhhhhh on 22 Jan 2025, 03:31, edited 1 time in total.
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Statement (1):
7/15 of the cars in the lot are blue.
Let the total number of cars = X.
Number of blue cars = (7/15) * X.
Given 50 < B < 60, find X such that (7/15) * X is an integer.
- If X = 120, B = (7/15) * 120 = 56 (valid).
No other value of X gives a valid B in the range.
Statement (1) is sufficient.
Statement (2):
B = blue cars, R = red cars.
B/R = 14/5 → B = (14/5) * R.
50 < B < 60 → 50 < (14/5) * R < 60.
Simplify:
250 < 14R < 300 → 17.857 < R < 21.428 → R = 18, 19, or 20.
- For R = 18: B = (14/5) * 18 = 50.4 (not valid).
- For R = 19: B = (14/5) * 19 = 53.2 (not valid).
- For R = 20: B = (14/5) * 20 = 56 (valid).
Total cars = B + R = 56 + 20 = 76.
Statement (2) is sufficient.
Final Answer: (D)
7/15 of the cars in the lot are blue.
Let the total number of cars = X.
Number of blue cars = (7/15) * X.
Given 50 < B < 60, find X such that (7/15) * X is an integer.
- If X = 120, B = (7/15) * 120 = 56 (valid).
No other value of X gives a valid B in the range.
Statement (1) is sufficient.
Statement (2):
B = blue cars, R = red cars.
B/R = 14/5 → B = (14/5) * R.
50 < B < 60 → 50 < (14/5) * R < 60.
Simplify:
250 < 14R < 300 → 17.857 < R < 21.428 → R = 18, 19, or 20.
- For R = 18: B = (14/5) * 18 = 50.4 (not valid).
- For R = 19: B = (14/5) * 19 = 53.2 (not valid).
- For R = 20: B = (14/5) * 20 = 56 (valid).
Total cars = B + R = 56 + 20 = 76.
Statement (2) is sufficient.
Final Answer: (D)
22 Jan 2025, 03:24
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Statement (1):
7/15 of cars in the lot are blue. Since 50<B<60, and the number of cars can be a whole number, the only number possible is 56 which is divisible by 7.
We can find out the total cars by
7/15 * x = 56.
x = 15 * 8 = 120.
Hence, Sufficient.
Statement (2):
The ratio of the number of blue cars to the number of red cars was 14 to 5.
We do not know anything about how many other car color's are present in the lot. There could be blue, black, white color cars too. Therefore Insufficient
[IMO] A.
7/15 of cars in the lot are blue. Since 50<B<60, and the number of cars can be a whole number, the only number possible is 56 which is divisible by 7.
We can find out the total cars by
7/15 * x = 56.
x = 15 * 8 = 120.
Hence, Sufficient.
Statement (2):
The ratio of the number of blue cars to the number of red cars was 14 to 5.
We do not know anything about how many other car color's are present in the lot. There could be blue, black, white color cars too. Therefore Insufficient
[IMO] A.
