If a 3-digit positive integer is a multiple of 7, what is the probabil

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Competition Mode Question

If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?

A. 1/7
B. 1/5
C. 11/54
D. 13/64
E. 13/66

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ArunSharma12 · Accepted Answer

If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?

A. 1/7
B. 1/5
C. 11/54
D. 13/64
E. 13/66

number 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

Enchanting · Answer

Smallest 3-digit number divisible by 7 = 105
 Largest 3-digit number divisible by 7 = 994
  We will use the sequence to find the number of 3-digit numbers divisible by 7
 994 = 105 + 7(n-1)  
 n = 128 
 The number which is divisible by 7 as well as 5 must be divisible by 35.
  Smallest 3-digit number divisible by 35 = 105
 Largest 3 digit number divisible by 35 = 980 
  Number of 3-digit multiples of 35
 980 = 105 + 35 , where 35 is the common difference and a is the number of multiple of 35.
 a = 26 
 Probability =  \frac{26}{128} =\frac{13}{64}  
Answer:  Option D.

freedom128 · Answer

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 = 13/64

FINAL ANSWER IS (D) 13/64

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unraveled · Answer

If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?

A. 1/7
B. 1/5
C. 11/54
D. 13/64
E. 13/66

So 100 < 7k < 999 (k is an integer)
14 < k < 142
k = 142 - 14 = 128

To 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' < 28
k' = 28 - 2 = 26

Probability =  \frac{26}{128} = \frac{13}{64}

Answer D.

madzaka · Answer

First one is 105 and is multiple
last one is 994 and is not multiple
994-105=889
889/7=127 and counting the first one is 128

For 5s and 7s are 105 as first and 980 as last that is 
980-105=875
875/35=25 with the first number 26

26/128=13/64

(D)

proy123 · Answer

D
multiple of 7-128
multiple of 35-26

pavankamatha · Answer

First triple digit multiple of 7: 7x15
last triple digit multiple of 7: 7x142

multiple of 7 and 5 have a form 7x5k .......(142/5)=28..............This includes 7x5 and 7x10.........hence 28-2 = 26
all multiples of 7 from 15 to 142........142-15+1 = 128

probabilty = 26/128 = 13/64 --------------------->  D

exc4libur · Answer

# of multiples from x to y:
largest(m)-smallest(m)/m+1

m of 7 from 100 to 999:
994-105/7+1=128

m of 7*5=35 from 100 to 999:
980-105/35+1=26

p(m35/m7's)=26/128=13/64

ans (D)

StevenA · Answer

If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?

A. 1/7
B. 1/5
C. 11/54
D. 13/64
E. 13/66

The 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}

Kinshook · Answer

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. 1/7
B. 1/5
C. 11/54
D. 13/64
E. 13/66

Multiple 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 = 26
3-digit multiples of 7 = {105,112,........994}; 3-digit Number of multiple of 7 = (994-105)/7 + 1 = 128

Probability = 26/128 = 13/64

IMO D

Archit3110 · Answer

for a 3 digit number to be a multiple of 7 & 5 it must be a factor of 35
so total multiple of 35 from 100 to 999; 26
and total multiples of 7 from 100 to 999 ; 128
so P = 26/128 ; 13/64
OPTION 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. 1/7
B. 1/5
C. 11/54
D. 13/64
E. 13/66

monikakumar · Answer

If a 3-digit positive integer is a multiple of 7, what is the probability that it will be a multiple of 5?

A. 1/7
B. 1/5
C. 11/54
D. 13/64
E. 13/66
 
3 digit from 105 to 994, n=994-105/7 = 127+1=128
128/5=26 (rounded off)
so prob=26/128=13/64
Ans D

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