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Founder  Joined: 18 Apr 2015
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How many different two-digit positive integers are there in [#permalink]
Expert's post 00:00

Question Stats: 70% (00:28) correct 29% (01:21) wrong based on 27 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]
2
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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.
_________________

Sandy
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Re: How many different two-digit positive integers are there in [#permalink]
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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
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Founder  Joined: 18 Apr 2015
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Re: How many different two-digit positive integers are there [#permalink]
1
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Expert's post
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

_________________ Manager Joined: 22 Feb 2018
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Re: How many different two-digit positive integers are there [#permalink]
1
KUDOS
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.
_________________ Manager Joined: 29 Nov 2017
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Re: How many different two-digit positive integers are there in [#permalink]
1
KUDOS
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.

Founder  Joined: 18 Apr 2015
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Kudos [?]: 1430 , given: 6569

Re: How many different two-digit positive integers are there in [#permalink]
Expert's post
Soon completed

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

Regards
_________________ Target Test Prep Representative Affiliations: Target Test Prep
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Re: How many different two-digit positive integers are there in [#permalink]
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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

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Manager Joined: 29 Nov 2017
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Re: How many different two-digit positive integers are there in [#permalink]
Carcass wrote:

where are other episodes??
Founder  Joined: 18 Apr 2015
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Re: How many different two-digit positive integers are there in [#permalink]
Expert's post
I have to jot down them _________________ Intern Joined: 23 Sep 2018
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Re: How many different two-digit positive integers are there in [#permalink]
2
KUDOS
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)
Manager Joined: 27 Feb 2017
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Re: How many different two-digit positive integers are there in [#permalink]
Oh dang! I totally forgot about the 0 GRE Instructor Joined: 10 Apr 2015
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Re: How many different two-digit positive integers are there in [#permalink]
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Expert's post
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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Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 14 Jan 2019
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Re: How many different two-digit positive integers are there in [#permalink]
How come this fell under the Tag of Hard Questions? It's pretty easy
Manager Joined: 27 Feb 2017
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Re: How many different two-digit positive integers are there in [#permalink]
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]
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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Manager Joined: 27 Feb 2017
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Re: How many different two-digit positive integers are there in [#permalink]
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?
Founder  Joined: 18 Apr 2015
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Re: How many different two-digit positive integers are there in [#permalink]
Expert's post
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]
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. Founder  Joined: 18 Apr 2015
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Re: How many different two-digit positive integers are there in [#permalink]
Expert's post
it is also logic

$$\frac{0}{number} = zero$$

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

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