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What is the value of the two-digit positive integer n?

(1) When n is divided by 5, the remainder is equal to the tens digit of n.

(2) When n is divided by 9, the remainder is equal to the tens digit of n.

Any help on this one would be much appreciated! Thanks

Let's take each statement at a time.

(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.

(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.

What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.

Re: What is the value of the two-digit positive integer n? [#permalink]

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18 Mar 2013, 11:21

clearly statement 1 leads to many options and same to statement 2

now taking both the statements together.

it should be a no. which is common multiple of both 5 and 9 and also is 2 digit no. which has 10th place digit as reminder... we have 9x5=45 so for reminder to be 4 the no. should be 49, which gives us reminder as 4. no other no. satisfies all the criteria mentioned in question.

clearly option C is answer
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Re: What is the value of the two-digit positive integer n? [#permalink]

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27 Jun 2013, 05:38

2

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alex1233 wrote:

What is the value of the two-digit positive integer n?

(1) When n is divided by 5, the remainder is equal to the tens digit of n.

(2) When n is divided by 9, the remainder is equal to the tens digit of n.

Any help on this one would be much appreciated! Thanks

we really dont need any calculation in this question. This is quite conceptual. we know remainder of any number when divided by 5 can only be 1,2,3 or 4.

Its given remainder equals to tens digit. we'll take the four remainders one by one.

1 >> we know tens digit should be 1 so number could only be 11 OR 16. 2 >> we know tens digit should be 2 so number could only be 22 OR 27 3 >> we know tens digit should be 3 so number could only be 33 OR 38. 4 >> we know tens digit should be 4 so number could only be 44 OR 49.

we cant get an answer from st. 1.

we can do same reasoning for st. 2 1 >> 10,19 2 >> 20,29 3 >> 30,39 4 >> 40,49 .... so on .. also no point going forward. we found a match from st. 1(and in st. 1 we wrote all the possible outcomes, so possibility of another such no. is zero) .. the no. is 49.

Re: What is the value of the two-digit positive integer n? [#permalink]

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15 Feb 2014, 15:30

VeritasPrepKarishma wrote:

alex1233 wrote:

What is the value of the two-digit positive integer n?

(1) When n is divided by 5, the remainder is equal to the tens digit of n.

(2) When n is divided by 9, the remainder is equal to the tens digit of n.

Any help on this one would be much appreciated! Thanks

Let's take each statement at a time.

(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.

(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.

What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.

Answer (C)

Hi Karishma,

I'm a bit stucked with both statements together. How do you know that the remainder has to be 4 and not 1,2 or 3?

What is the value of the two-digit positive integer n?

(1) When n is divided by 5, the remainder is equal to the tens digit of n.

(2) When n is divided by 9, the remainder is equal to the tens digit of n.

Any help on this one would be much appreciated! Thanks

Let's take each statement at a time.

(1) When n is divided by 5, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 5 - say 15. The remainder should be 1 so say n = 16. Think of another number which is divisible by 5 - say 25. The remainder should be 2 so say n = 27 There will be more such numbers so we can see that this is certainly not sufficient.

(2) When n is divided by 9, the remainder is equal to the tens digit of n. Think of a two digit number which is divisible by 9 - say 18. The remainder should be 1 so say n = 19. Think of another number which is divisible by 9 - say 27. The remainder should be 2 so say n = 29 There will be more such numbers so we can see that this is certainly not sufficient.

What do we do when we consider both statements together? We need to think of a number divisible by both 5 and 9, say 45 (their LCM). The remainder should be 4 so add 4 to 45 to get n = 49 Think of another number divisible by both which will be the next multiple of 45 i.e. 90. The remainder should be 9 but when we divide a number by 5, the remainder cannot be greater than 4. So n cannot be 99. Hence, there is only one such two digit number i.e. n = 49.

Answer (C)

Hi Karishma,

I'm a bit stucked with both statements together. How do you know that the remainder has to be 4 and not 1,2 or 3?

Could you please elaborate on this?

Many thanks! Cheers J

The tens digit of 45 is 4. 45 is the first positive two digit number which is divisible by both 5 and 9. So when n is divided by 5 or 9, the remainder should be 4 so n should be 49. The remainder will be 4 which is the tens digit of 49.
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16 Sep 2015, 08:54

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