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Re: Is the positive two-digit integer N less than 40 ? [#permalink]
03 Dec 2012, 04:45

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Is the positive two-digit integer N less than 40 ?

(1) The units digit of N is 6 more than the tens digit --> the greatest possible value of the units digit is 9, thus the greatest possible value of the tens digit is 9-6=3, which means that N is less than 40. Sufficient.

(2) N is 4 less than 4 times the units digit. The same here: the greatest possible value of the units digit is 9, thus the greatest possible value of N is 4*9-4=32. Sufficient.

Re: Is the positive two-digit integer N less than 40 ? [#permalink]
03 Dec 2012, 07:14

I solved it using method of substitution.

Given number(N) is 2 digit number. So, 0<N<100. So, Question is whether N<40

Case 1: If Number N is AB, AB => A (A+6). AB => 17,28,39. hence, For sure, Number is less than 40. Option is sufficient to answer the question.

As Option A is sufficient to answer the question, Answer Choices C, E are eliminated.

Case 2: N is 4 less than 4 times the units digit. Let's N is AB N=> 4*B-4 => 4*(B-1) So, B should be greater than 5. If B =5, N =4 (Invalid case) If B =6, N =8 (Invalid case) IF B =7, N =24 If B =8, N =28 If B =9, N =32. So, For sure Number is less than 40. Option is sufficient to answer the question.

So, Either statement is sufficient to answer this question.

Re: Is the positive two-digit integer N less than 40 ? [#permalink]
30 Dec 2012, 02:39

When considering statement 2, isn't 28 the only correct number?

When units digit is 8, (4*units)-4 = (4*8)-4 = 32 - 4 = 28

The units digit of N=28 is also 8. So technically, N=24 or N=32 do not even satisfy the condition. But for DS, I guess (4*9)-4 is the fastest and best way.

Re: Is the positive two-digit integer N less than 40 ? [#permalink]
30 Dec 2012, 05:58

Expert's post

th03 wrote:

When considering statement 2, isn't 28 the only correct number?

When units digit is 8, (4*units)-4 = (4*8)-4 = 32 - 4 = 28

The units digit of N=28 is also 8. So technically, N=24 or N=32 do not even satisfy the condition. But for DS, I guess (4*9)-4 is the fastest and best way.

You are right: 28 is the only two-digit number which satisfies the second statement.

Re: Is the positive two-digit integer N less than 40 ? [#permalink]
12 Jan 2014, 08:30

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Re: Is the positive two-digit integer N less than 40 ? [#permalink]
26 Jun 2014, 23:13

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Let no. be TU. (T- Ten's digit, U - Unit's digit). Also, since these are digits of a number & using the given constraint, 0<=U<=9, 1<=T<=9.

Required: 1<=T<=3 Constraints: 0<=U<=9, 1<=T<=9

A: U = T + 6 => T = U-6. Using constraints, U = 9,8,7; 1<=T<=9. This also results in 1<=T<=3. Hence, sufficient. B: 10T + U = 4U - 4 => T = (3U - 4)/10. Using constraints, U = 8; 1<=T<=9. This also results in 1<=T<=3. Hence, sufficient.

Thus, D.

gmatclubot

Re: Is the positive two-digit integer N less than 40 ?
[#permalink]
26 Jun 2014, 23:13