It is currently 19 Apr 2019, 07:03

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

How many different two-digit positive integers are there

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 6185
Followers: 99

Kudos [?]: 1199 [0], given: 5699

How many different two-digit positive integers are there in [#permalink]  05 Mar 2017, 08:58
Expert's post
00:00

Question Stats:

70% (00:29) correct 30% (01:03) wrong based on 20 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

_________________
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 106

Kudos [?]: 1819 [2] , given: 397

Re: How many different two-digit positive integers are there in [#permalink]  11 Mar 2017, 17:13
2
KUDOS
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
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GRE Instructor
Joined: 10 Apr 2015
Posts: 1644
Followers: 57

Kudos [?]: 1570 [2] , given: 8

Re: How many different two-digit positive integers are there in [#permalink]  15 Oct 2017, 15:29
2
KUDOS
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
Posts: 6185
Followers: 99

Kudos [?]: 1199 [1] , given: 5699

Re: How many different two-digit positive integers are there [#permalink]  22 Feb 2018, 13:46
1
KUDOS
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
Posts: 160
Followers: 2

Kudos [?]: 105 [1] , given: 22

Re: How many different two-digit positive integers are there [#permalink]  22 Feb 2018, 17:39
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
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 78 [1] , given: 99

Re: How many different two-digit positive integers are there in [#permalink]  11 May 2018, 07:27
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
Posts: 6185
Followers: 99

Kudos [?]: 1199 [0], given: 5699

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

Regards
_________________
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 131 [1] , given: 0

Re: How many different two-digit positive integers are there in [#permalink]  18 May 2018, 10:05
1
KUDOS
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
22 Reviews

5-star rated online GRE quant
self study course

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews

Manager
Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 78 [0], given: 99

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

where are other episodes??
Founder
Joined: 18 Apr 2015
Posts: 6185
Followers: 99

Kudos [?]: 1199 [0], given: 5699

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
_________________
Intern
Joined: 23 Sep 2018
Posts: 6
Followers: 0

Kudos [?]: 4 [2] , given: 0

Re: How many different two-digit positive integers are there in [#permalink]  23 Sep 2018, 23:11
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
Posts: 189
Followers: 0

Kudos [?]: 51 [0], given: 15

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
GRE Instructor
Joined: 10 Apr 2015
Posts: 1644
Followers: 57

Kudos [?]: 1570 [1] , given: 8

Re: How many different two-digit positive integers are there in [#permalink]  22 Jan 2019, 06:39
1
KUDOS
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:

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Intern
Joined: 14 Jan 2019
Posts: 31
Followers: 0

Kudos [?]: 8 [0], given: 5

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
Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 0

Kudos [?]: 51 [0], given: 15

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.

Founder
Joined: 18 Apr 2015
Posts: 6185
Followers: 99

Kudos [?]: 1199 [0], given: 5699

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
_________________
Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 0

Kudos [?]: 51 [0], given: 15

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?
Founder
Joined: 18 Apr 2015
Posts: 6185
Followers: 99

Kudos [?]: 1199 [0], given: 5699

Re: How many different two-digit positive integers are there in [#permalink]  02 Feb 2019, 03:23
Expert's post
Of course, sorry I assumed was implied that zero was an integer
_________________
Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 0

Kudos [?]: 51 [0], given: 15

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.
Founder
Joined: 18 Apr 2015
Posts: 6185
Followers: 99

Kudos [?]: 1199 [0], given: 5699

Re: How many different two-digit positive integers are there in [#permalink]  02 Feb 2019, 03:39
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
Display posts from previous: Sort by