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14 Oct 2021, 04:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:03) correct
38%
(02:13)
wrong
based on 232
sessions
History
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Not Attempted Yet
In a horse show, nine of the horses competing were awarded ribbons. The show’s judge never awards ribbons to fewer than 15% of the horses and never to more than 30% of the horses. If h is the number of horses competing, how many different values of h are possible?
(A) 15
(B) 16
(C) 24
(D) 30
(E) 31
(A) 15
(B) 16
(C) 24
(D) 30
(E) 31
25 Oct 2021, 03:52
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Bunuel
Let \(x\) be the MOST number of horses possible
Then \(\frac{15}{100}*x = 9 -> x= 60 \)
Let \(y\) be the LEAST number of horses possible
Then \(\frac{30}{100}*y = 9 -> y= 30 \)
Hence we cannot have fewer than \(30\) and more than \(60 \) horses.
All integers from \(30\) to \(60\) inclusive are possible values of h
Hence \(60-30 +1 = 31\) Horses
Ans=E
Hope it's clear.
25 Oct 2021, 06:14
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Bunuel
Breaking Down the Info:
Set the number of horses as \(h\).
"never awards ribbons to fewer than 15% of the horses": The 9 ribbons must represent at least 15% of the horses.
\(\frac{9}{h} \geq 15\%\), which is \(h \leq \frac{9}{15\%} = 60\).
"never to more than 30% of the horses": The 9 ribbons must represent at most 30% of the horses.
\(\frac{9}{h} \leq 30\%\), which is \(h \geq \frac{9}{30\%} = 30\).
Then combined, we have \(30 \leq h \leq 60\). Double-check that we include the end-points.
Note 31 to 60 inclusive would be 30 numbers, so 30 to 60 inclusive would be 31 numbers.
Answer: E
