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Let n be the largest integer that is the product of exactly 3 distinct

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Bunuel
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Let n be the largest integer that is the product of exactly 3 distinct [#permalink] Let n be the largest integer that is the product of exactly 3 distinct   19 Mar 2019, 02:30
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Let n be the largest integer that is the product of exactly 3 distinct prime numbers d, e, and 10d + e, where d and e are single digits. What is the sum of the digits of n ?

(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
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Let n be the largest integer that is the product of exactly 3 distinct [#permalink] Let n be the largest integer that is the product of exactly 3 distinct   19 Mar 2019, 04:42
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Bunuel wrote:
Let n be the largest integer that is the product of exactly 3 distinct prime numbers d, e, and 10d + e, where d and e are single digits. What is the sum of the digits of n ?

(A) 12
(B) 15
(C) 18
(D) 21
(E) 24


Let me start this question by thinking the biggest two digit prime numbers (to find biggest possibility of 10d+e) whose both digits (d and e) are prime

The umber can't be in 90's or 80's as 8 and 9 are non-prime digits

so the number may be 73 where d = 7 and e = 3

i.e. n = 3*7*73 = 1533

Sum of digits of n = 1+5+3+3 = 12

Answer: Option A
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Re: Let n be the largest integer that is the product of exactly 3 distinct [#permalink] Let n be the largest integer that is the product of exactly 3 distinct   19 Mar 2019, 10:32
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Bunuel wrote:
Let n be the largest integer that is the product of exactly 3 distinct prime numbers d, e, and 10d + e, where d and e are single digits. What is the sum of the digits of n ?

(A) 12
(B) 15
(C) 18
(D) 21
(E) 24


d,e, * 10d+3 are all prime no
so largest no which would be possible 7,3,73
product = 1533 ; sum of digits= 12
IMO A
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Let n be the largest integer that is the product of exactly 3 distinct [#permalink] Let n be the largest integer that is the product of exactly 3 distinct   01 Mar 2021, 19:49
Consider the primes less than 10: 2, 3, 5, 7
The question asks for the largest integer that is the product of d, e, and 10d+e so we'll start by making d=7

We can have 72, 73, 75, of which, 73 is the only prime and thus will maximize the product we're trying to find
7*3*73 = 21*73 = 1533 and the sum of its digits is 1+5+3+3 = 12

Answer (A)
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Let n be the largest integer that is the product of exactly 3 distinct [#permalink]
01 Mar 2021, 19:49
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