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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

10 May 2012, 04:45

2

This post was BOOKMARKED

Hey everyone. As you can see, I need help with something so simple. I'm sure the answer is right in front of me and I can't see it. They use the above question in Manhattan Number Properties. They start listing multiples: 105, 112,119,126, 133, 140, 147. The thing that is not clear to me is how I know to start with 105 instead of say, 103 or 101.

The first multiple of 7 that is greater than 100, is 105. (70+35 = 105). The one before that is 98, and that's less than 100.

This is the most reliable way to solve the question (listing). Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

10 May 2012, 05:37

bb wrote:

The first multiple of 7 that is greater than 100, is 105. (70+35 = 105). The one before then is 98, and that's less than 100.

This is the most reliable way to solve the question (listing). Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Hey everyone. As you can see, I need help with something so simple. I'm sure the answer is right in front of me and I can't see it. They use the above question in Manhattan Number Properties. They start listing multiples: 105, 112,119,126, 133, 140, 147. The thing that is not clear to me is how I know to start with 105 instead of say, 103 or 101.

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

19 Mar 2014, 12:47

bb wrote:

The first multiple of 7 that is greater than 100, is 105. (70+35 = 105). The one before that is 98, and that's less than 100.

This is the most reliable way to solve the question (listing). Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Hope this helps.

Why does the (last - first) / increment rule not always work here? I know it doesn't (for example, count the number of multiples of 7 between 11 and 24. There are two (14, 21), but (last - first) / increment gives you 1.

Also, the Manhattan GMAT book lists (last - first) / increment + 1 as the rule to use here, but that doesn't always work either. For example, count the number of multiples between 9 and 24. There are two: 14, and 21. But (last - first) / increment + 1 is gives you 3 multiples.

It appears that in these sorts of problems involving the number of multiples between two numbers: we cannot strictly rely on formulas and instead need to think them through on a case by case basis, right?

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

19 Mar 2014, 20:23

1

This post was BOOKMARKED

onewayonly wrote:

bb wrote:

The first multiple of 7 that is greater than 100, is 105. (70+35 = 105). The one before that is 98, and that's less than 100.

This is the most reliable way to solve the question (listing). Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Hope this helps.

Why does the (last - first) / increment rule not always work here? I know it doesn't (for example, count the number of multiples of 7 between 11 and 24. There are two (14, 21), but (last - first) / increment gives you 1.

Also, the Manhattan GMAT book lists (last - first) / increment + 1 as the rule to use here, but that doesn't always work either. For example, count the number of multiples between 9 and 24. There are two: 14, and 21. But (last - first) / increment + 1 is gives you 3 multiples.

It appears that in these sorts of problems involving the number of multiples between two numbers: we cannot strictly rely on formulas and instead need to think them through on a case by case basis, right?

Thanks.

The formula is NOT just "last - first," but the actual formula is "last MULTIPLE in range - first MULTIPLE in range." Here is the complete formula:

\(# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1\).

Using one of your examples, you stated: "count the number of multiples of 7 between 11 and 24. There are two (14, 21), but (last - first) / increment gives you 1."

This would be solved like this: \(\frac{21 - 14}{7}+1 = 2\)

Using your other example, you stated: "count the number of multiples between 9 and 24. There are two: 14, and 21. But (last - first) / increment + 1 is gives you 3 multiples." I'm assuming you meant "count the number of multiples of 7" between the range of 9 and 24 (you didn't specify the multiple in this example).

This would be solved using the exact same numbers as shown in the above example. Once again, the answer would be 2.

@onewayonly The last and first term refer to the terms of an arithmetic sequence, and you have to make sure that all the terms are part of an arithmetic sequence, where the difference between successive terms is fixed. In the case of counting multiples, you have to start with the first multiple in the range and the last multiple in the range, we can't just use the first and last term of the given range.

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

24 Mar 2014, 04:16

For such questions : Last term is the last multiple within the range and the first term is the first multiple within the range. This series of multiples forms an AP sequence.

Lets understand the formula \(((Last term - First term)/ spacing) +1\) We get this formula from AP(Arithmetic Progression) formula for last term i.e Tn = a + (n - 1) d

Lets take the first term as 'a' and the nth term as 'b'

Using the formula for nth term of an AP, we get : b = a + (n - 1)d. We need the value of 'n'. Solving we get : \(n = ((b - a)/d)+1\) where, b = last term , a = first term, and d = common difference.

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

09 Jun 2016, 15:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

23 Oct 2017, 02:36

1

This post received KUDOS

bb wrote:

The first multiple of 7 that is greater than 100, is 105. (70+35 = 105). The one before that is 98, and that's less than 100.

This is the most reliable way to solve the question (listing). Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Hope this helps.

bb Could you please explain where this method is from? and why it does not work very well? Thank you! >> Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

29 Oct 2017, 13:19

1

This post received KUDOS

1

This post was BOOKMARKED

gracecud46 wrote:

Could you please explain where this method is from? and why it does not work very well? Thank you! >> Another is to subtract 100 from 150 and divide that by 7 but that does not always work well. In this case, it does since 50 divided by 7 is 7.

So in the question, the multiples of 7 between 100 and 150 are: 105, 112, 119, 126, 133, 140, and 147 which means that there are seven multiples of 7 between 100 and 150

(150-100)/7 = 50/7 = 7 remainder 1, so if you drop the remainder you would get the same answer as we did counting above by subtracting the upper limit of the range from the lower limit and dividing by the factor.

bb says this is a dangerous method, because what if I asked you "how many multiples of 7 are there between 104 and 155?" The answer would be 105, 112, 119, 126, 133, 140, 147, and 154 which equals eight.

Using the alternative method, I would get (155 -104)/7 = 51/7 = 7 remainder 2, dropping the remainder gives me an answer of seven which is the wrong answer to my new question.

I hope this adds some clarity to why bb said this method does not work very well, or at least it does not work very reliably. In the original case you would get the correct answer, however in the similar case I presented you would get the wrong answer.

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

14 Nov 2017, 15:50

1

This post received KUDOS

The most efficient way would be to recognize that 105=70+35. You can use the following approach if it doesn't come to you right away:

Divide 100 by 7, your remainder is 2. Since 2+5 is 7, adding 5 to 100 will make it divisible by 7.
_________________

Source: We are an NYC based, in-person and online GMAT tutoring company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to ask us a question!

Re: How many multiples of 7 between 100 and 150? [#permalink]

Show Tags

29 Nov 2017, 23:40

1

This post received KUDOS

If we divide 100 by 7, we get remainder = 2. Since 2+5 = 7, adding 5 to 100 will make it divisible by 7 and that is 105. Similarly if we divide 150 by 7, we get remainder = 3, so if we remove 3 from 150 we get the largest number less than 150 that is divisible by 150. To calculate the number of terms in Arithmetic Progression, we use: a+(n-1)d=last term where a=first term n=number of terms d=constant difference between any two successive terms =>105+(n-1)7=147 =>(n-1)7=42 =>n-1=42/7=6 =>n=7 Therefore the number of multiples of 7 between 105 and 147 (inclusive)= 7

In this example as the number of terms are 7, we can do it manually. However, for a larger sequence we need to use Arithmetic Progression formula.

Today we’re excited to announce two new premium themes: Small Business and Photo Blog . Small Business Small Business is a new premium theme for your entrepreneurial endeavors. At...

As part of our commitment to privacy and transparency, we’re updating our Privacy Policy . We want to give you more and clearer information about how we collect and use...

Product Leadership is a book that distills the best practices of Product Management into one source. Mark Ericsson is the founder of Product Tank and Mind the Product and...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...