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# How many different two-digit positive integers are there in

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How many different two-digit positive integers are there in [#permalink]  05 Mar 2017, 08:58
Expert's post
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Question Stats:

77% (00:33) correct 22% (00:40) wrong based on 45 sessions

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]  11 Mar 2017, 17:13
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Expert's post
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]  15 Oct 2017, 15:29
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Expert's post
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

[Reveal] Spoiler:
D

Cheers,
Brent
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Re: How many different two-digit positive integers are there in [#permalink]  11 May 2018, 07:27
1
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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

[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.

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Re: How many different two-digit positive integers are there in [#permalink]  12 May 2018, 07:49
Expert's post
Soon completed

https://greprepclub.com/forum/all-you-n ... -8898.html

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Re: How many different two-digit positive integers are there in [#permalink]  18 May 2018, 10:05
1
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Expert's post
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.

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Re: How many different two-digit positive integers are there in [#permalink]  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]  22 May 2018, 12:09
Expert's post
I have to jot down them
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Re: How many different two-digit positive integers are there in [#permalink]  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]  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]  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.

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]  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]  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.

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Re: How many different two-digit positive integers are there in [#permalink]  02 Feb 2019, 03:16
Expert's post
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]  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]  02 Feb 2019, 03:23
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Of course, sorry I assumed was implied that zero was an integer
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Re: How many different two-digit positive integers are there in [#permalink]  02 Feb 2019, 03:29
Carcass wrote:
Of course, sorry I assumed was implied that zero was an integer

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.
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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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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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