Find the lower bound and upper bound that is a multiple of 7! so for a three digit integer that is a multiple of 7, 100 is the lowest possible three digit integer and 999 is the highest, however, neither of these are a multiple of 7! So starting at 100 find a multiple of 7! (105) is the product of (15*7), that is your lower bound. Now find your upper bound,starting at 999; you find, (994) which is a product of (142*7)! Now use a THEOREM (IF m and n are integers, and m <= n,then there are n-m +1 integers from m to n, inclusive). This means take the integer 142 from the product of 142*7 from your upper bound, and subtract that from your lower bound product which is the integer 15 from the product 15*7. You will get your event (E) so E = 142 - 15 + 1 = 128. So E = 128, that is how many three digit integers are a multiple of 7! So now take your E and put that over your sample space (S) where S = all possible outcomes in a random outcomes. so (s) = 9 * 10 * 10 where the first digit of your three digit number is a natural number between 1-9, the second digit can be any natural number from 0 to 9, and the third digit number can also be a natural number between 0 and 9. So you get (S) = 9 * 10 * 10 = 900. So E/S gives you your ratio or probability of number of three digit integers that are a multiple of 7. You can use this for any three digit multiple, or four digit multiple ... (N) multiple where N is a non negative member of Z.
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?A. 1/7B. 1/5C. 11/54D. 13/64E. 13/66number of multiples of 7 = \(\frac{999}{7}-\frac{100}{7} = 142 - 14 = 128\)number of multiples of 35 =\(\frac{999}{35}-\frac{100}{35} = 28 - 2 = 26\) probability that a multiple of 7 will be a multiple of 5 = \(\frac{26}{128}\) = \(\frac{13}{64}\) Ans: D
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink]
n = 128
Largest 3 digit number divisible by 35 = 980
a = 26
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] 3-digit positive integer is a multiple of 7: 105, 112, 119,..., 994. Calculating 994 = 105 + (n-1)*7, we know that 994 is the 128th (=n) element of the series.3-digit positive integer that is both a multiple of 5 and 7: 105, 140, 175,..., 980.Calculating 980 = 105 + (n-1)*35, we know that 980 is the 26th (=n) element of the series.Thus, the probability that it will be both multiple of 5 and 7 is 26/128 = 13/64FINAL ANSWER IS (D) 13/64 Posted from my mobile device
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?A. 1/7B. 1/5C. 11/54D. 13/64E. 13/66So 100 < 7k < 999 (k is an integer)14 < k < 142k = 142 - 14 = 128To find whether these numbers are a multiple of 5, we need to check for LCM(5,7) = 35 multiplicity. Also, 100 < 35k' < 999 (k' is an integer)2 < k' < 28k' = 28 - 2 = 26Probability = \(\frac{26}{128} = \frac{13}{64}\)Answer D. _________________
Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] First one is 105 and is multiplelast one is 994 and is not multiple994-105=889889/7=127 and counting the first one is 128For 5s and 7s are 105 as first and 980 as last that is 980-105=875875/35=25 with the first number 2626/128=13/64 (D)
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] Dmultiple of 7-128 multiple of 35-26
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] First triple digit multiple of 7: 7x15last triple digit multiple of 7: 7x142multiple of 7 and 5 have a form 7x5k .......(142/5)=28..............This includes 7x5 and 7x10.........hence 28-2 = 26all multiples of 7 from 15 to 142........142-15+1 = 128 probabilty = 26/128 = 13/64 ---------------------> D
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink]
Quote: If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?A. 1/7B. 1/5C. 11/54D. 13/64 E. 13/66 # of multiples from x to y:largest(m)-smallest(m)/m+1m of 7 from 100 to 999:994-105/7+1=128m of 7*5=35 from 100 to 999:980-105/35+1=26p(m35/m7's)=26/128=13/64ans (D)
Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?A. 1/7B. 1/5C. 11/54D. 13/64E. 13/66The probability that the 3-digit positive integer is a multiple of both 5 and 7 are -> \(\frac{P(both 5 and 7)}{p(7 only)}\)# 3 digits number multiple of 7 --> An = a + (n-1) b --> 994 = 105 + (n-1) x 7 --> n = 128# 3 digits number multiple of 7 and 5 --> An = a + (n-1) b --> 980 = 105 + (n-1) x 35 --> n = 26 Hence, the ratio is \(\frac{26}{128}\) = \(\frac{13}{64}\)
Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] Asked: If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?A. 1/7B. 1/5C. 11/54D. 13/64E. 13/66Multiple of 7 which is also a multiple of 5 = multiple of 35 = {105,145,......980}; 3-digit Number of multiple of 35 = (980-105)/35 + 1 = 263-digit multiples of 7 = {105,112,........994}; 3-digit Number of multiple of 7 = (994-105)/7 + 1 = 128Probability = 26/128 = 13/64IMO D _________________
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] for a 3 digit number to be a multiple of 7 & 5 it must be a factor of 35so total multiple of 35 from 100 to 999; 26and total multiples of 7 from 100 to 999 ; 128so P = 26/128 ; 13/64OPTION D If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?A. 1/7B. 1/5C. 11/54D. 13/64 E. 13/66
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?A. 1/7B. 1/5C. 11/54D. 13/64E. 13/66 3 digit from 105 to 994, n=994-105/7 = 127+1=128128/5=26 (rounded off)so prob=26/128=13/64 Ans D
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Re: If a 3-digit positive integer is a multiple of 7, what is the probabil [#permalink] 31 Dec 2021, 06:14 |
What is the probability that a three digit number that is a multiple of 7 is also multiple of 5?
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