How many multiples of 33 lie between 101 and 1,000, inclusiv

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu Sep 20, 2018 12:53 am

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[Math Revolution GMAT math practice question]

How many multiples of 33 lie between 101 and 1,000, inclusive?

A. 24
B. 27
C. 33
D. 36
E. 48

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 20, 2018 5:17 am

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

How many multiples of 33 lie between 101 and 1,000, inclusive?

A. 24
B. 27
C. 33
D. 36
E. 48

Some positive multiples of 33 are: 33, 66, 99, 132, 165, 198,. . . , 957, 990, 1023
So, we want the number of multiples of 33 from 132 to 990 inclusive

Observe:
132 = (33)(4)
165 = (33)(5)
198 = (33)(6)
.
.
.
957 = (33)(29)
990 = (33)(30)

We can see that the number of multiples of 33 from 132 to 990 inclusive is the SAME as the number of integers from 4 to 30 inclusive.

To determine the above, we can apply the following rule: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 4 to 30 inclusive = 30 - 4 + 1 = 27

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 20, 2018 5:21 am

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

How many multiples of 33 lie between 101 and 1,000, inclusive?

A. 24
B. 27
C. 33
D. 36
E. 48

Another approach is to apply the following rule:

If x and y are multiples of k, then the number of multiples of k from x to y inclusive = [(y-x)/k] + 1
So, for example, the multiples of 3 from 6 to 21 inclusive = [(21 - 6)/3] + 1 = [15/3] + 1 = 6

So, the number of multiples of 33 from 132 to 990 inclusive = (990 - 132)/33 + 1
= 858/33 + 1
= 26 + 1
= 27

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Sep 20, 2018 5:31 am

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

How many multiples of 33 lie between 101 and 1,000, inclusive?

A. 24
B. 27
C. 33
D. 36
E. 48

Since 1000 - 101 â‰ˆ 900 -- and the answer choices are a bit spread out -- we can count the multiples of 33 simply by dividing 33 into 900:
900/33 = 300/11 = a bit more than 27.
Thus, there are 27 multiples of 33 between 101 and 1000.

The correct answer is B.

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Sep 20, 2018 7:03 am

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

How many multiples of 33 lie between 101 and 1,000, inclusive?

A. 24
B. 27
C. 33
D. 36
E. 48

One of our studentsÂ´ most-loved mottos is: let the "Queen of Sciences" (Mathematics) do the weight-lifting for you!
\[? = M\,\,\,\left( {\operatorname{int} } \right)\]
\[101 < 33M < 1000\]
\[\left( {99 + 33 = } \right)\,\,\,132 \leqslant 33M \leqslant 990\,\,\,\,\left( { = 30 \cdot 33} \right)\]
\[4 \leqslant M \leqslant 30\,\,\,\, \Rightarrow \,\,\,\,? = 30 - 4 + 1 = 27\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

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English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Mon Sep 24, 2018 4:08 am

=>
Consider the arithmetic sequence 132, 165, ..., 990 of multiples of 33.
The number of terms in this sequence is (990-132)/33 + 1 = 858 / 33 + 1 = 26 + 1 = 27.

Therefore, the answer is B.
Answer: B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8198; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Sep 27, 2018 4:23 pm

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

How many multiples of 33 lie between 101 and 1,000, inclusive?

A. 24
B. 27
C. 33
D. 36
E. 48

The smallest multiple of 33 above 101 is 132 and the largest multiple of 33 below 1,000 is 990.

So the number of multiples is:

(990 - 132)/33 + 1 = 27

Answer: B

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