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Manager  Joined: 02 Dec 2012
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Is the positive two-digit integer N less than 40 ?  [#permalink]

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Question Stats: 63% (02:03) correct 37% (02:13) wrong based on 2559 sessions

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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.
Math Expert V
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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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]

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11
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]

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2
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]

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1
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.

D
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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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]

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2
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]

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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]

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2
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]

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1
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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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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(1) N=ab (a and b are digits and a>0)
Possible values can be 39, 28, and 17.
All less than 40.

Sufficient.

(2) If b is 9 (the highest digit), then N=32 which is less than 40.

Sufficient.

D
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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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.

Can you please explain why B has to be greater than 5?
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Is the positive two-digit integer N less than 40 ?  [#permalink]

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2
Just list the digits and check

Statement one-The units digit of N is 6 more than the tens digit
For a 2 digit no the choice available for 10's place is 1 to 9 and for units it is 0 to 9

List down all combinations starting from 1 where the units digit is 6 more than 10's

17
28
39
Sufficient- lets check one more combination-4+(4+6)=4+10=14-does not meet question condition.

Statement Two- N is 4 less than 4 times the units digit

Again list down units digits starting with 9

9*4-4= 32- Not valid as in 32 the units digit is 2 and as per the statement-4*2-4=4
8*4-4=28-Valid
7*4-4=24-not valid and so on

Hence sufficient since only one no ie 28 meets the statement 2 condition and is less than 40.
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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Top Contributor
2
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.

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

Cheers,
Brent
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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If we form equation for the 2 statements separately, the answer is C. This is what I have done -
From Statement 1, since the units digit is 6 more than the tens digit, so we can write like this N=10x+6, where x can take 1,2 and 3 as values.
From Statement 2, N-4 = 4u, where u is integer where u<=8.

Solving above two, 36 is the only value coming from both the equations so answer is C. Please explain and correct me if I made any mistakes.
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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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.

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.

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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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If the maximum value of the unit digit could be 9 and 9-6= 3 , can you please tell me why is N less than 40? We know just that the unit digit of the number is 3 so could be 13-23-33-43-53 etc...
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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MathRevolution wrote:
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.

For A,
Why cant we make it as 11x+6 as N? In thatcase we get diffrent values?
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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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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) The units digit of N is 6 more than the tens digit.
--> possible numbers = 17, 28, 39
--> All are < 40

Sufficient

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

Take maximum value of unit digit = 9
--> N < 4*9 - 4
--> N < 32

Sufficient

IMO Option D

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Re: Is the positive two-digit integer N less than 40 ?  [#permalink]

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Que - positive two-digit integer N less than 40 ?

statement (1) The units digit of N is 6 more than the tens digit
17 , 28 ,39 are values that will come
which means that N is less than 40. Sufficient.

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

greatest value of N is 4*9-4=32. Sufficient.
0thers 8 * 4 - 4 = 28 there after also < 40 Re: Is the positive two-digit integer N less than 40 ?   [#permalink] 21 Jun 2019, 20:18

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