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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Let P(n) and S(n) denote the product and the sum, respectively, of the

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Math Expert V
Joined: 02 Sep 2009
Posts: 59725
Let P(n) and S(n) denote the product and the sum, respectively, of the  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 71% (02:08) correct 29% (02:06) wrong based on 35 sessions

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Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What is the units digit of N?

(A) 2
(B) 3
(C) 6
(D) 8
(E) 9

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Intern  B
Joined: 09 Feb 2019
Posts: 4
Let P(n) and S(n) denote the product and the sum, respectively, of the  [#permalink]

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Bunuel wrote:
Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What is the units digit of N?

(A) 2
(B) 3
(C) 6
(D) 8
(E) 9

I am solving this question by assuming values

Say N = 29
P(N) = 18
S(N) = 11

In this case N = P(N) + S(N)
29 = 18 + 11

So the Unit digit is 9. IMO E.
We can check for other values as well.
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Let P(n) and S(n) denote the product and the sum, respectively, of the  [#permalink]

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4
Bunuel wrote:
Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What is the units digit of N?

(A) 2
(B) 3
(C) 6
(D) 8
(E) 9

N= 10a+b
N = P(N) + S(N)
= a+b+ab
10a+b=a+b+ab
9a=ab
b=9
IMO E
Target Test Prep Representative V
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Posts: 8701
Location: United States (CA)
Re: Let P(n) and S(n) denote the product and the sum, respectively, of the  [#permalink]

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Bunuel wrote:
Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What is the units digit of N?

(A) 2
(B) 3
(C) 6
(D) 8
(E) 9

We can create the equation in which A = the tens place of the number and B = the ones place (i.e., units digit). Thus, the two-digit number can be expressed as 10A + B, the product of the two digits is AB, and the sum of the two digits is A + B. Using N = P(N) + S(N), we have:

10A + B = AB + A + B

10A = AB + A

9A = AB

9 = B

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Let P(n) and S(n) denote the product and the sum, respectively, of the   [#permalink] 19 Mar 2019, 19:09
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# Let P(n) and S(n) denote the product and the sum, respectively, of the  