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# How many multiples of 7 are there between 700 and 1000, inclusive?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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26 Sep 2016, 03:01
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Difficulty:

25% (medium)

Question Stats:

76% (01:14) correct 24% (01:42) wrong based on 193 sessions

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How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20

_________________
Retired Moderator
Joined: 26 Nov 2012
Posts: 592
How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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26 Sep 2016, 05:38
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20

This is how I tried...

There are exactly 301 numbers between 700 to 1000..

701 to 800 = 100
801 to 1000 = 200...Total 300 numbers , count 700 too..

301/7 = 43...

IMO option A.
Intern
Joined: 10 Jan 2014
Posts: 8
GMAT 1: 600 Q40 V31
Re: How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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26 Sep 2016, 06:05
1
2
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20

Smallest 7 digit number divisible by 7 = 700 here
Largest div by 7 = 994

994-700 = 294
Now, 294/7 = 42

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How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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26 Sep 2016, 10:24
3
anki2762 wrote:
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20

Smallest 7 digit number divisible by 7 = 700 here
Largest div by 7 = 994

994-700 = 294
Now, 294/7 = 42

Arithmetic Progression Approach !!!

Please correct the Highlighted part in RED ... I am sure U meant Number divisible by 7 and Not 7 Digit Number...

Now, in the AP series - { 700, 707, 714............994 }

$$a$$ = 700 ( Smallest Number )
$$d$$ = 7 ( common Difference )
$$l$$ = 994 ( Largest Number )

No of Terms = $$\frac{( l - a )}{d} + 1$$

No of Terms = $$\frac{( 994 - 700 )}{d} + 1$$

No of Terms = $$42+ 1$$

No of Terms = $$43$$

Hence answer will be (A) 43

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Re: How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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21 Jul 2018, 02:45
msk0657 wrote:
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20

This is how I tried...

There are exactly 301 numbers between 700 to 1000..

701 to 800 = 100
801 to 1000 = 200...Total 300 numbers , count 700 too..

301/7 = 43...

IMO option A.

Even though your approach seems bizarre, you have got the right answer. One should find the least and the largest number that is divisible by 7. The least number between 700-1000 that is the multiple of 7 is 700 and the largest is 994. We subtract 700 from 994 to get the numbers of the range, which is 294. Meanwhile, the inclusion means that we should also take into account 994 itself. When we count the possibilities through 294, we ignore 994 itself.
In the range of 1-10, when you subtract 10-1=9 which itself omits 10 from the range. The same applies to the problem.
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Director
Joined: 19 Oct 2013
Posts: 508
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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07 Sep 2018, 17:13
Two ways of solving the above question

either $$1,000 - 700 = 300 + 1 = \frac{301}{7} = 43$$
or $$100*7 = 700$$ and $$142 * 7 = 994$$ then $$142 - 100 = 42 + 1 = 43$$
Senior SC Moderator
Joined: 22 May 2016
Posts: 2496
How many multiples of 7 are there between 700 and 1000, inclusive?  [#permalink]

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07 Sep 2018, 19:01
Bunuel wrote:
How many multiples of 7 are there between 700 and 1000, inclusive?

A. 43
B. 42
C. 22
D. 21
E. 20

To find the number of terms, we can use
$$\frac{LastTerm-FirstTerm}{Increment}+1$$

(Some people use the quip "add one before you're done.")

First Term: $$700$$

Last Term? Divide 1,000 by 7

1)$$\frac{1,000}{7}=42.xx$$. That is, (42*7) is the highest we can go
2) So the Last Term is $$(42*7)=994$$

Number of terms? Increment = 7: $$(\frac{994-700}{7}+1)=(\frac{294}{7}+1)=(42+1)=43$$

For an excellent post on sequences, including how to find number of terms, see Guide to Sequences and Series, HERE (scroll to Part 2 for Number of Terms)

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How many multiples of 7 are there between 700 and 1000, inclusive?   [#permalink] 07 Sep 2018, 19:01
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