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605-655 (Medium)|   Arithmetic|                              
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shwetasood
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Is the positive two-digit integer N less than 40 ? 04 Oct 2023, 18:37
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umeshpatil
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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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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Engineer1
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Is the positive two-digit integer N less than 40 ? 15 Jan 2024, 13:46
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Bunuel
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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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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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Is the positive two-digit integer N less than 40 ? 15 Jan 2024, 14:09
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Engineer1
Bunuel
th03
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!
Show more

(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 ? 15 Jan 2024, 14:26
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Bunuel

(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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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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Is the positive two-digit integer N less than 40 ? 04 Apr 2025, 22:46
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Walkabout
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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For the 2nd case, if we take units digit as 0,
N = (4*0) - 4 = -4 (which is not a positive integer).

Wouldn't this mean that Case 2 is NOT SUFFICIENT
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