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.

Answer: D.
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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.

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

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

There are 3 variables (n,a,b) and 1 equation (n=10a+b) in the original condition, 2 equations in the given conditions, making it likely that (C) will be our answer.
Looking at the conditions,
For 1, n=17,28,39<40 answers the question yes, and is therefore sufficient.
For 2, 10a+b=4b-4, 10a+4=3b, and this answers the question 'yes' for n=28<40. This is sufficient as well, making the answer seem like (D).
However, this is a logic question with commonly made mistake type 4(B).

Hence, (C) also becomes the answer but if we apply integer commonly made mistake type 4, the answer still becomes (D).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Can you please explain why B has to be greater than 5?

Target question: Is N less than 40

Given: N is a positive two-digit integer

Statement 1: The units digit of N is 6 more than the tens digit
This statement is, essentially, restricting the value of the tens digit.
If the units digit is 6 more than the tens digit, then the tens digit cannot be very big.
For example, the tens digit cannot be 8, because the units digit would have to be 14, which is impossible.
Likewise, the tens digit cannot be 4, because the units digit would have to be 10, which is also impossible.
So, the greatest possible value of the tens digit of N is 3.
As such, N must be less than 40
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: N is 4 less than 4 times the units digit.
Well, 9 is the greatest possible value of any integer, and if the units digit were 9, then N would equal (4)(9) - 4, which is less than 40
So, no matter what value the units digit has, the resulting number (N), must be less than 40
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:
Cheers,
Brent
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We need to determine whether the positive two-digit integer N is less than 40.

Statement One Alone:

The units digit of N is 6 more than the tens digit.

With the information in statement one, we know the units digit is the larger of the two digits in N. So let’s say the units digit is 9 (the largest digit possible); then the tens digit will be 3 (since 9 is 6 more than 3). Thus this makes N = 39, which is less than 40. Now let’s say the units digit is 8; then the tens digit will be 2 and thus N = 28, which is still less than 40. Let’s say the units digit is 7; then the tens digit will be 1 and thus N = 17, which is again less than 40. At this point, we can’t make the units digits any smaller; if we did, the tens digits would be 0 or negative, but we know N is a positive two-digit integer.

Statement one is sufficient to answer the question.

Statement Two Alone:

N is 4 less than 4 times the units digit.

Again, let’s test some possible numerical values for the units digit. Let’s start with 9 again since it’s the largest digit possible. If the units digit is 9, then N = 4(9) – 4 = 32, which is less than 40. If the units digit is any smaller, then N will be less than 32, which means N will always be less than 40. If you can’t see this, look at the following:

If the units digit is 8, then N = 4(8) – 4 = 28.

If the units digit is 7, then N = 4(7) – 4 = 24, etc.

Statement two is also sufficient to answer the question.

Answer: D
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