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If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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25 Dec 2017, 01:41
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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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25 Dec 2017, 03:28
Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 When x is a multiple of 4 for eg. 4,8,12.... then there are 25 such numbers between 0<x≤100 when x+1 is a multiple of 4 i.e x=4k1 (where k is some constant) for eg. 3,7,11....., then again there will be 25 such numbers between 0<x≤100 So total numbers of the form x(x+1) that are multiple of 4 =25+25=50 So probability \(= \frac{50}{100}=\frac{1}{2}\) Option D



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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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25 Dec 2017, 06:12
Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 Solution Given:• The variable x is greater than 0, but less than or equal to 100.
o The values of x can be 1,2,3,…..so on till 100. o Thus we can say that the total possible values of x are 100. Find: • We are given the expression x (x+1) and we need to find the probability that the expression x(x+1) is a multiple of 4. Approach:• Since x and (x+1) are consecutive numbers, both cannot be even or a multiple of 4. • For x to be a multiple of 4, either x or x+1 has to be a multiple of 4. • Thus, let us look at the two possible cases:
o x is a multiple of 4.
x = 4k and k can be 1,2,3,4….till 25 Since x = 4 * 25 = 100, thus the last value of k will be 25 And total possible values can be 25. o (x + 1) is a multiple of 4.
x + 1 = 4q x = 4q 1 Thus, the values of q can be 1,2,3 and so on till…25 and the value of x will be 3,7…99 Even in this case, the total possible values are 25. • Thus, total favourable cases = 25 + 25 = 50 • And the probability that x(x+1) = Favorable cases/ Total case = 50/100 = 1/2 The correct answer is Option D.
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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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25 Dec 2017, 16:57
Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 From 1 to 100 there are: \(Number.Terms=Last.termFirst.term+1=1001+1=100\) total outcomes. If x is a multiple of 4 then x(x+1) = multiple of 4. If x+1 is a multiple of 4 then x(x+1) = multiple of 4. From 1 to 100 there are: \(Number.Multiples=\frac{Largest.multipleSmallest.multiple}{Multiple}+1=\frac{1004}{4}+1=25\) multiples of 4 that fit \(x\), and \(25\) multiples of 4 that fit \(x1\). Probability is: \(\frac{Favorable.Outcomes}{Total.Outcomes}=\frac{(25+25)}{100}=1/2\). (D) is the answer.



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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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Updated on: 26 Dec 2017, 10:17
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Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 Hi EgmatQuantExpert, niks18, chetan2u, Can you please help me to clarify my doubt. The question states that \(0 < x ≤ 100\), so for all the Integers value of \(x\) the answer will be \(\frac{50}{100}\). However, here x can be decimals also for ex  \(x\)= \((\sqrt{17}1)/2\), x = \((\sqrt{65}1)/2\). Can you please let me know if I am missing anything here.
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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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26 Dec 2017, 09:46
rahul16singh28 wrote: Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 Hi EgmatQuantExpert, niks18, chetan2u, Can you please help me to clarify my doubt. The question states that \(0 < x ≤ 100\), so for all the Integers value of \(x\) the answer will be \(\frac{50}{100}\). However, here x can be decimals also for ex  \(x\)= \(\frac{\sqrt{17[}{square_root]1/2}\), x = \([square_root]65}1/2\). Can you please let me know if I am missing anything here. Hi rahul16singh28Here x is a multiple of 4. Multiples of 4 cannot be decimals (0.4=2/5 is not a multiple of 4), they will have to be an integer. so probability has to be between favorable integer values which are (25+25) and total integers possible which is 100



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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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26 Dec 2017, 09:47
X = 4,8,....100  25 count X+1 = 4,8,.....100 25 count
Total = 25 + 25 = 50
Answer : 50/100 = 1/2



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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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26 Dec 2017, 09:52
niks18 wrote: rahul16singh28 wrote: Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 Hi EgmatQuantExpert, niks18, chetan2u, Can you please help me to clarify my doubt. The question states that \(0 < x ≤ 100\), so for all the Integers value of \(x\) the answer will be \(\frac{50}{100}\). However, here x can be decimals also for ex  \(x\)= \(\frac{\sqrt{17[}{square_root]1/2}\), x = \([square_root]65}1/2\). Can you please let me know if I am missing anything here. Hi rahul16singh28Here x is a multiple of 4. Multiples of 4 cannot be decimals (0.4=2/5 is not a multiple of 4), they will have to be an integer. so probability has to be between favorable integer values which are (25+25) and total integers possible which is 100 Hi niks18, I think here we have to find out if x(x+1) is a multiple of 4. If we take \(x\)= \(\sqrt{17}1/2\), then x(x+1) is a multiple of 4.
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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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26 Dec 2017, 10:02
Quote: Hi niks18, I think here we have to find out if x(x+1) is a multiple of 4. If we take \(x\)= \(\sqrt{17}1/2\), then x(x+1) is a multiple of 4. Hi rahul16singh28if \(x= \sqrt{17}\frac{1}{2}\), then \(x+1=\sqrt{17}\frac{1}{2}+1=\sqrt{17}+\frac{1}{2}\) now \(x(x+1)=(\sqrt{17}\frac{1}{2})(\sqrt{17}+\frac{1}{2})=17\frac{1}{4}\) which is not a multiple of \(4\). Point is non integers cannot be multiples of integers otherwise every non integer can be multiple of integer



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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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26 Dec 2017, 10:15
niks18 wrote: Quote: Hi niks18, I think here we have to find out if x(x+1) is a multiple of 4. If we take \(x\)= \(\sqrt{17}1/2\), then x(x+1) is a multiple of 4. Hi rahul16singh28if \(x= \sqrt{17}\frac{1}{2}\), then \(x+1=\sqrt{17}\frac{1}{2}+1=\sqrt{17}+\frac{1}{2}\) now \(x(x+1)=(\sqrt{17}\frac{1}{2})(\sqrt{17}+\frac{1}{2})=17\frac{1}{4}\) which is not a multiple of \(4\). Point is non integers cannot be multiples of integers otherwise every non integer can be multiple of integer Hi niks18, May be I am missing something silly here but what I meant was if \(x\)= \((\sqrt{17}  1)/2\). True that nonintegers cannot be multiple of Integer but here we have a case where product of 2 noninteger (x & x+1) is a multiple of integer for \(x\)= \((\sqrt{17}  1)/2\) and this is what exactly we need to find.
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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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26 Dec 2017, 10:18
rahul16singh28 wrote: Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 Hi EgmatQuantExpert, niks18, chetan2u, Can you please help me to clarify my doubt. The question states that \(0 < x ≤ 100\), so for all the Integers value of \(x\) the answer will be \(\frac{50}{100}\). However, here x can be decimals also for ex  \(x\)= \((\sqrt{17}1)/2\), x = \((\sqrt{65}1)/2\). Can you please let me know if I am missing anything here. It was missing in the question that x is an integer.
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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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26 Dec 2017, 10:20
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Bunuel wrote: rahul16singh28 wrote: Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 Hi EgmatQuantExpert, niks18, chetan2u, Can you please help me to clarify my doubt. The question states that \(0 < x ≤ 100\), so for all the Integers value of \(x\) the answer will be \(\frac{50}{100}\). However, here x can be decimals also for ex  \(x\)= \((\sqrt{17}1)/2\), x = \((\sqrt{65}1)/2\). Can you please let me know if I am missing anything here. It was missing in the question that x is an integer. rahul16singh28 our problem is solved



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Re: If x is an integer and 0 < x ≤ 100, what is the probability that x(x + [#permalink]
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29 Dec 2017, 23:33
rahul16singh28 wrote: Bunuel wrote: If 0 < x ≤ 100, what is the probability that x(x + 1) is a multiple of 4?
A. 1/8 B. 1/4 C. 33/100 D. 1/2 E. 29/50 Hi EgmatQuantExpert, niks18, chetan2u, Can you please help me to clarify my doubt. The question states that \(0 < x ≤ 100\), so for all the Integers value of \(x\) the answer will be \(\frac{50}{100}\). However, here x can be decimals also for ex  \(x\)= \((\sqrt{17}1)/2\), x = \((\sqrt{65}1)/2\). Can you please let me know if I am missing anything here. I solved this question with the assumption that x is an integer. You did the right thing by not assuming it in the starting and considering all the possible cases. But given that GMAT does not test us on such complex matters, I felt that assuming x is an integer makes sense and it might just be miss a while framing the question, which Bunuel did clarify. Regards, Saquib eGMAT Quant Expert
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