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E
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Difficulty:
95%
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Question Stats:
49% (02:40) correct
51%
(02:20)
wrong
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If\(p\) is an integer such that \(\dfrac{p}{24}=33,\!463.625\), what is the remainder when \(p\) is divided by \(48\)?
(A) \(5\)
(B) \(13\)
(C) \(15\)
(D) \(24\)
(E) \(39\)
(A) \(5\)
(B) \(13\)
(C) \(15\)
(D) \(24\)
(E) \(39\)
Updated on: 20 Jul 2026, 05:17
Originally posted by MartyMurray on 19 Jul 2026, 06:44.
Last edited by MartyMurray on 20 Jul 2026, 05:17, edited 1 time in total.
Last edited by MartyMurray on 20 Jul 2026, 05:17, edited 1 time in total.
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If \(\dfrac{p}{24}=33,463.625\), what is the remainder when \(p\) is divided by \(48\)?
\(p = 24 × 33,463.625 = 24 × (33,462 + 1.625) = (48 × \frac{33,462}{2}) + (24 × 1.625)\)
\(24 × 1.625 = 24 × 1 \frac{5}{8} = 39\)
(A) \(5\)
(B) \(13\)
(C) \(15\)
(D) \(24\)
(E) \(39\)
Correct answer: E
\(p = 24 × 33,463.625 = 24 × (33,462 + 1.625) = (48 × \frac{33,462}{2}) + (24 × 1.625)\)
\(24 × 1.625 = 24 × 1 \frac{5}{8} = 39\)
(A) \(5\)
(B) \(13\)
(C) \(15\)
(D) \(24\)
(E) \(39\)
Correct answer: E
19 Jul 2026, 07:04
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kevincan
\(\frac{p}{24} = 33463.625\)
\(\frac{p}{24} = 33463+0.625\)
\(\frac{p}{24} = 33462+1+0.625\)
\(p = 24(33462+1+0.625)\)
\(p = (24*33462)+24+ (24* 0.625)\)
\(p = (24*33462)+24+ (24* \frac{625}{1000})\)
\(p = (24*33462)+24+ (24* \frac{25}{40})\)
\(p = (24*33462)+24+ (24* \frac{5}{8})\)
\(p = (24*33462)+24+ (5*3)\)
\(p = (24*33462)+24+ 15\)
\(p = (24*33462)+39\)
Remainder(p/48) = Remainder {(24*33462)/48} + Remainder (39/48)
24*33462 is divisible by 48
Remainder(p/48) = 0 + Remainder (39/48)
= 39
Option E
