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

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Is the positive two-digit integer N less than 40 ? [#permalink]  03 Dec 2012, 04:42
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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.
(2) N is 4 less than 4 times the units digit.
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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.

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Re: Is the positive two-digit integer N less than 40 ? [#permalink]  03 Dec 2012, 07:14
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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.
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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.
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Re: Is the positive two-digit integer N less than 40 ? [#permalink]  30 Dec 2012, 03:56
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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.
(2) N is 4 less than 4 times the units digit.

1.Max 39 so suff

2. N = 4U-4 = 4(U-1) so basically all multiple of 4 in two digits where U can be anything from 3<U<=9 so a max of 32 so Suff.

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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.
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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.
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Re: Is the positive two-digit integer N less than 40 ? [#permalink]  23 Oct 2014, 02:49
umeshpatil wrote:
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.

B=5 --> N=4*(B-1) = 4*(5-1)= 16 valid case
similarly
B=6 --> N=4*(B-1) = 4*(6-1)= 20 valid case

just wanted to correct you.

this in no way changes the answer but might confuse someone. So just trying to help.

Kudos if you appreciate it.
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Re: Is the positive two-digit integer N less than 40 ? [#permalink]  23 Oct 2014, 05:20
Is the positive two-digit integer N less than 40 ?

(1) The units digit of N is 6 more than the tens digit.
(2) N is 4 less than 4 times the units digit.

D.

1) let N = ab
=> b = a+6
b can maximum be 9, in which case a would be 3 (N = 39 max)
so N < 40 - Yes.
sufficient.

2) let N = ab
=> 10a+b - 4 = 4b
=> 10a-3b = 4
(a,b) = (1,2) is the only valid solution
so N < 40 - Yes
sufficient.
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Re: Is the positive two-digit integer N less than 40 ?   [#permalink] 23 Oct 2014, 05:20
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