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How many different two-digit positive integers are there

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How many different two-digit positive integers are there in [#permalink] New post 05 Mar 2017, 08:58
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How many different two-digit positive integers are there in which the tens digit is greater than 6 and the units digit is less than 4 ?

A) 7

B) 9

C) 10

D) 12

E) 24
[Reveal] Spoiler: OA

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Re: How many different two-digit positive integers are there in [#permalink] New post 11 Mar 2017, 17:13
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Explanation

There are three possibilities for the tens digit: 7, 8, and 9.
There are four possibilities for the units digit: 0, 1, 2, and 3.

3 possibilities × 4 possibilities = 12

Hence option D is correct.
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Re: How many different two-digit positive integers are there in [#permalink] New post 15 Oct 2017, 15:29
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Carcass wrote:


How many different two-digit positive integers are there in which the tens digit is greater than 6 and the units digit is less than 4 ?

A) 7

B) 9

C) 10

D) 12

E) 24


If you're not sure how to begin, start listing possible outcomes

How do I know this is a reasonable strategy?
Because the answer choices are relatively small.

The numbers that meet the conditions are: 70, 71, 72, 73, 80, 81, 82, 83, 90, 91, 92, and 93
TOTAL = 12

Answer:
[Reveal] Spoiler:
D


Cheers,
Brent
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Re: How many different two-digit positive integers are there [#permalink] New post 22 Feb 2018, 13:46
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Explanation

If you read the stem step by step very carefully the solution is pretty quick.

different two-digit positive integers are there in which the tens digit is greater than 6 = 7,8,9

units digit is less than 4 = 0,1,2,3. For istance: 70,71,72, 73. These number that are 4 for 3 times (7,8,9) we do have 12

D is the answer.
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Re: How many different two-digit positive integers are there [#permalink] New post 22 Feb 2018, 17:39
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answer: D
integers are positive and two digits like 17, 68, 97, etc. in the two digits positive integers tens digit is the one with power 1, in the 17: tens digit is 1. In the 68: tens digit is 6. The question wants numbers which their tens digit is more than 6, Thus their tens digit can be 7, 8 and 9. Units digit is the digit with power 0, in 17: unit digit is 7, in 68: unit digit is 8. Unit digit must be less than 4, So it can be 0, 1, 2, 3.
So we can have 7,8,9 in the tens digit and 0,1,2,3 in the unit digit. Possible numbers are:
70, 71, 72, 73
80, 81, 82, 83
90, 91, 92, 93
there are 12 numbers with these circumstances.
*unit digit is the digit with power 0, tens digit is the digit with power 1, etc.
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Re: How many different two-digit positive integers are there in [#permalink] New post 11 May 2018, 07:27
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GreenlightTestPrep wrote:
Carcass wrote:


How many different two-digit positive integers are there in which the tens digit is greater than 6 and the units digit is less than 4 ?

A) 7

B) 9

C) 10

D) 12

E) 24


If you're not sure how to begin, start listing possible outcomes

How do I know this is a reasonable strategy?
Because the answer choices are relatively small.

The numbers that meet the conditions are: 70, 71, 72, 73, 80, 81, 82, 83, 90, 91, 92, and 93
TOTAL = 12

Answer:
[Reveal] Spoiler:
D


Cheers,
Brent




can you please tell, when should one look at the option choices, I avoid looking at them before I derive the solution myself, often it is wrong and at the testing conditions it makes me panic when I see that my answer is not the listed one.. in such case I pick the one which is closest to mine answer..which is more often wrong approach..

when should I consider OPTION CHOICES in order to derive the at the solution ... can you also share a link to GRE MATHS STRATEGIES.

Thanks in advance.
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Re: How many different two-digit positive integers are there in [#permalink] New post 12 May 2018, 07:49
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Re: How many different two-digit positive integers are there in [#permalink] New post 18 May 2018, 10:05
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Carcass wrote:


How many different two-digit positive integers are there in which the tens digit is greater than 6 and the units digit is less than 4 ?

A) 7

B) 9

C) 10

D) 12

E) 24


If the tens digit is greater than 6, there are 3 options (7, 8, 9) for the tens digit. If the units digit is less than 4, there are 4 options (3, 2, 1, 0) for the units digit, so we have a total of 3 x 4 = 12 ways to create the number.

Answer: D
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Re: How many different two-digit positive integers are there in [#permalink] New post 21 May 2018, 06:28
Carcass wrote:


where are other episodes??
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Re: How many different two-digit positive integers are there in [#permalink] New post 22 May 2018, 12:09
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I have to jot down them :wink:
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Re: How many different two-digit positive integers are there in [#permalink] New post 23 Sep 2018, 23:11
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For a 2 digit positive integer, if the ten's digit has to be greater than 6 - possibilities are 7,8,9(3 options)

Similarly, if the one's digit has to be less than 4 - possibilities are 0,1,2,3 (4 options)

Therefore, the two digit numbers possible are 3*4 = 12(Option D)
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Re: How many different two-digit positive integers are there in [#permalink] New post 22 Jan 2019, 06:21
Oh dang! I totally forgot about the 0
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Re: How many different two-digit positive integers are there in [#permalink] New post 22 Jan 2019, 06:39
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IshanGre wrote:
can you please tell, when should one look at the option choices, I avoid looking at them before I derive the solution myself, often it is wrong and at the testing conditions it makes me panic when I see that my answer is not the listed one.. in such case I pick the one which is closest to mine answer..which is more often wrong approach..

when should I consider OPTION CHOICES in order to derive the at the solution ... can you also share a link to GRE MATHS STRATEGIES.

Thanks in advance.


You should ALWAYS check the answer choices BEFORE performing any calculations. There are many reasons for this (see video below), but here's a rudimentary example:

Let's say you have a counting question, and you recognize that the answer will equal 26^3
Let's also say the answer choices are:
A) 17,572
B) 17,573
C) 17,574
D) 17,575
E) 17,576

If we try head straight to the online calculator (or start multiplying 26x26x26 on scratch paper), we're missing out on a 1-second answer.

Since all powers of 26 will have 6 as a units digit, we know that the correct answer is E

For more on this, watch:

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Re: How many different two-digit positive integers are there in [#permalink] New post 23 Jan 2019, 20:50
How come this fell under the Tag of Hard Questions? It's pretty easy
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Re: How many different two-digit positive integers are there in [#permalink] New post 02 Feb 2019, 00:59
I have a big question regarding the concept of this question. I am looking at some questions involving integers that are not considering 0 as a positive integer. Here is an example from Barrons Model paper test 2:

Q. A number x is chosen at random from the set of integers less than 10. What is the probability that 9/x > x?

I considered 0 as a positive integer and got 3/10. But the explanation does not consider 0 and the correct answer is 2/9.

Please help what to do in such cases?
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Re: How many different two-digit positive integers are there in [#permalink] New post 02 Feb 2019, 03:16
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If a question such as the example you provided above says this, then it is really flawed.

Universal math law: zero is even and neither positive nor negative
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Re: How many different two-digit positive integers are there in [#permalink] New post 02 Feb 2019, 03:19
Carcass wrote:
If a question such as the example you provided above says this, then it is really flawed.

Universal math law: zero is even and neither positive nor negative


So, do we consider 0 as an integer or no?
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Re: How many different two-digit positive integers are there in [#permalink] New post 02 Feb 2019, 03:23
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Of course, sorry I assumed was implied that zero was an integer :roll:
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Re: How many different two-digit positive integers are there in [#permalink] New post 02 Feb 2019, 03:29
Carcass wrote:
Of course, sorry I assumed was implied that zero was an integer :roll:


Thanks for clearing it up. I saw a couple of conflicting theories from different sources. But I will go with what you and ETS say. It is the safest. :-D
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Re: How many different two-digit positive integers are there in [#permalink] New post 02 Feb 2019, 03:39
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it is also logic

\(\frac{0}{number} = zero\)

\(\frac{number}{zero} = \infty\) (infinity) which is not accepted

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Re: How many different two-digit positive integers are there in   [#permalink] 02 Feb 2019, 03:39
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