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

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.

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.

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 a digit, 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: D

Cheers,
Brent

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

Could you help me by combining both statements, please?
Thanks__

Sure.

To elaborate more: the question does not ask: what is the greatest possible value of N. The question asks: is N less than 40. From both statements we get an YES answer for the question, because even the greatest possible value of N from each statement is less than 40.

If you combine the statements, N turns out to be 28.

From (1) N could be: 39, 28, or 17.
From (2) N could be only 28.

Answer: Option D

Video solution by GMATinsight

EMPOWERgmatRichC
Dear Rich,
could you outline the error in my approach?
https://gmatclub.com/forum/is-the-posit ... l#p2877231

Thanks beforehand.

Hi BLTN,

Based on the information in Fact 2, the units digit of N CANNOT be 9. Here's why:

IF... the units digit of N was 9, then "4 less than 4 times the units digit would be.... 4(9) - 4 = 36 - 4 = 32.... meaning that N = 32.... but 32 has a units digit of '2' (and in this example, it's supposed to be a '9'). Thus, this is NOT a valid example that fits the information in Fact 2.

That having been said, what this example DOES prove is that whatever 2-digit number that N could be, that option (or options) MUST be LESS than 32 (since the largest possible units digit is '9' - and by extension, the largest possible value of N cannot be any greater than the resulting 32). Notice how the question asks "if... N is less than 40?" This bit of work - even though it technically does not 'fit' the information in Fact 2 - does provide enough evidence that N will ALWAYS be less than 40 (and more specifically, N will ALWAYS be less than 32).

GMAT assassins aren't born, they're made,
Rich

Hi Bunuel, I get the explanation but I am still a little confused.
Statement 1 says that unit digit of N is 6 more than tens digit. I can't stop thinking about this statement. According to my translation, If the greates vale of units digit is 9 then the tens digit is 6 less than the units digit so 97
Similarly, if unit digit of N is 8 then tens digit will be 2 there for N is 82.

Statement 2 makes sense.

What am i getting wrong?

Say N is ab, where a is the tens digit and b is the units digit.

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

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

Hope it's clear.

BrentGMATPrepNow

For statement 2, I understand the logic you provide but I'm not sure whether we need to find a possible or satisfied value of N, because if there was no single number of N that satisfy statement 2 and the question, statement 2 would be wrong.

This is where we have to pay extra attention to the target question.
Here, the target question asks Is N less than 40?

So, even though statements 2 allows for several different values of N, every one of those possible N-values is less than 40, which means we can answer the target question with certainty: YES, N less is definitely than 40
Since we can answer the target question with certainty, statement 2 is sufficient.

Does that help?

I understand your point : if we know that the maximum of unit number, which is 9, can make the N less than 40. Thus, every one of those possible N-values is less than 40. But what If there is no any number less than 40 ? I mean if there is no any number that can satisfy the condition in statement 2. Thus, if we use the logic you provide, do we need to check is there at least 1 number that satisfy the condition in statement2 ?

If statement 2 yielded a bunch of possible N-values that were all greater than 40, then the statement 2 would be sufficient, because we would be able to answer the target question with certainty.
In this case the answer would be "NO, N is not less than 40"

Hi Tanchat,

DS prompts are designed so that there will ALWAYS be AT LEAST ONE value that fits the given information in Fact 1 or Fact 2 (or Both). Part of your job when solving DS prompts is to determine whether there is more than one answer or not (and to always be thinking in terms of the specific question that is asked).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]