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How many multiples of 33 lie between 101 and 1,000, inclusive?
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20 Sep 2018, 02:04
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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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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?
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20 Sep 2018, 02:13
MathRevolution wrote: [ Math Revolution GMAT math practice question] How many multiples of \(33\) lie between \(101\) and \(1,000,\) inclusive? \(A. 24\) \(B. 27\) \(C. 33\) \(D. 36\) \(E. 48\) First multiple of 33 in the range : 132 (33*4)
Last Multiple in the range : 990 (33*30)
No. of multiple in the range : (304) + 1 = 27.
The best answer is B.



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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?
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20 Sep 2018, 06:19
MathRevolution 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 + 1So, the number of integers from 4 to 30 inclusive = 30  4 + 1 = 27 Answer: B Cheers, Brent
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?
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20 Sep 2018, 06:23
MathRevolution 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 = [(yx)/k] + 1So, for example, the multiples of 3 from 6 to 21 inclusive = [(21  6)/3] + 1 = [15/3] + 1 = 6So, 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
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?
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20 Sep 2018, 06:34
MathRevolution 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 ≈ 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.
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How many multiples of 33 lie between 101 and 1,000, inclusive?
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20 Sep 2018, 08:07
MathRevolution 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 students´ mostloved mottos is: let the "Queen of Sciences" (Mathematics) do the weightlifting for you! \(101 < 33M < 1000\) \(? = M\,\,\,\left( {\operatorname{int} } \right)\) \(\left( {99 + 33 = } \right)\,\,\,132 \leqslant 33M \leqslant 990\,\,\,\,\left( { = 30 \cdot 33} \right)\) \(4 \leqslant M \leqslant 30\,\,\,\, \Rightarrow \,\,\,\,? = 30  4 + 1 = 27\) This solution follows the notations and rationale taught in the GMATH method. Regards, fskilnik. P.S.: that´s EXACTLY Selim´s solution, only a bit more "structured". Congrats, Selim!!
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?
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24 Sep 2018, 06:12
=> Consider the arithmetic sequence \(132, 165, …, 990\) of multiples of \(33\). The number of terms in this sequence is \(\frac{(990132)}{33} + 1 =\frac{858}{33} + 1 = 26 + 1 = 27.\) Therefore, the answer is B. Answer: B
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