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Posts: 6218
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N is a positive 3-digit integer in which all three digits ha
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10 Jul 2019, 12:23
10 Jul 2019, 12:23
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N is a positive 3-digit integer in which all three digits have the same value. The product 53N is a 5-digit integer comprised of five of the following six digits: 1, 2, 4, 6, 7, 9
Which of the following digits is NOT in the product 53N?
A) 1
B) 2
C) 4
D) 6
E) 7
Which of the following digits is NOT in the product 53N?
A) 1
B) 2
C) 4
D) 6
E) 7
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: N is a positive 3-digit integer in which all three digits ha
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11 Jul 2019, 05:22
11 Jul 2019, 05:22
1
GreenlightTestPrep wrote:
N is a positive 3-digit integer in which all three digits have the same value. The product 53N is a 5-digit integer comprised of five of the following six digits: 1, 2, 4, 6, 7, 9
Which of the following digits is NOT in the product 53N?
A) 1
B) 2
C) 4
D) 6
E) 7
Which of the following digits is NOT in the product 53N?
A) 1
B) 2
C) 4
D) 6
E) 7
KEY PROPERTY #1: There's a nice divisor property that says: If n is divisible by d, then kn is divisible by d (assuming n, d and k are INTEGERS)
For example, since 33 is divisible by 11, we also know that (33)(7) is divisible by 11
Since 111 is divisible by 3, we know that (2)(111) is divisible by 3, and (3)(111) is divisible by 3, and (4)(111) is divisible by 3, and (5)(111) is divisible by 3, etc.
In other words, we know that N is divisible by 3.
So, from property #1, we also know that 53N is divisible by 3.
KEY PROPERTY #2: If a number is divisible by 3, the sum of its numbers is also be divisible by 3
So, we must choose 5 numbers (from 1, 2, 4, 6, 7, 9) so that the sum of the digits is divisible by 3.
1 + 2 + 4 + 6 + 7 + 9 = 29
So, if we DON'T select the digit 2, the remaining digits add to 27, which IS divisible by 3.
Answer: B
Cheers,
Brent
Re: N is a positive 3-digit integer in which all three digits ha
[#permalink]
18 Aug 2019, 01:26
18 Aug 2019, 01:26
Hello,
I understood the rule, but i didn't get how you conclude 53N is divisible by 3.
Can you please elaborate?
I understood the rule, but i didn't get how you conclude 53N is divisible by 3.
Can you please elaborate?
