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

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Difficulty: 605-655 Levelx   Arithmeticx                              
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Re: Is the positive two-digit integer N less than 40 ? [#permalink] New post   04 Oct 2023, 18:37
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.




Hi, in your solution in case 2, if B=5 then N is supposed to be 16
and if B=6 then N is supposed to be 20
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Re: Is the positive two-digit integer N less than 40 ? [#permalink] New post   15 Jan 2024, 13:46
Bunuel wrote:
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.



Bunuel chetan2u

Not sure why 28 is the only correct answer to statement 2. I am curious.
Anyhow, all answers are < 40, so B is sufficient.

N = 10a+ b (N = ab format)
N = 4b -4
b = 1 and 2 give invalid values of N (one digit number)
Therefore, with b = 3,4,5,...,9, N = 12, 16, 20, 24,....32 (Each < 40).

Why are 24 or 32 invalid? Thanks!
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Re: Is the positive two-digit integer N less than 40 ? [#permalink] New post   15 Jan 2024, 14:09
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Engineer1 wrote:
Bunuel wrote:
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.



Bunuel chetan2u

Not sure why 28 is the only correct answer to statement 2. I am curious.
Anyhow, all answers are < 40, so B is sufficient.

N = 10a+ b (N = ab format)
N = 4b -4
b = 1 and 2 give invalid values of N (one digit number)
Therefore, with b = 3,4,5,...,9, N = 12, 16, 20, 24,....32 (Each < 40).

Why are 24 or 32 invalid? Thanks!


(2) says: N is 4 less than 4 times the units digit.

How does 24 or 32 satisfy (2)?

You should have done: 10a + b = 4b - 4, which gives 10a = 3b - 4.
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Is the positive two-digit integer N less than 40 ? [#permalink] New post   15 Jan 2024, 14:26
Bunuel wrote:
(2) says: N is 4 less than 4 times the units digit.

How does 24 or 32 satisfy (2)?

You should have done: 10a + b = 4b - 4, which gives 10a = 3b - 4.


Whoa, did not think of it that way. The question could be tweaked to be more complicated, such as - what is the value of N? Thank you!
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