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What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?

A.

1/15

B.

2/15

C.

4/15

D.

7/15

See Answer & Explanation Lets Discuss
Correct answer is : C
Explanation

Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30

 

Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.

For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.

So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6

 

Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24

 

So total probability = 24/90 = 4/15

 

spandana 3/17/2014 6:33:14 PM

pls explain in broad the first line in explanation?...

Indhumathi 4/30/2014 1:48:31 PM

Pls explain that in the first line how 90 came and also why we have to add 1 to find the numbers which are divisible by 5?

Jashu 8/1/2014 10:46:30 AM

since given that  number is a two digit number . the two digit numbers start from 10 and end with 99.In total there are 90 numbers

ramireddy 8/9/2014 7:54:16 PM

pls explain in broad the first line in explanation?..

nilesh purohit 8/14/2014 1:41:59 PM

1st line i understood n explain next in brief plz

 

manish 8/16/2014 2:20:40 AM

how 1 added to 5 please explain

basha 8/18/2014 1:37:18 PM

sir plz explain in brief

Tamil selvi 8/22/2014 7:24:57 AM

For example if we want to know the number wich is divisible by both 2 and 3 surely it is multiple of 2 and 3 witch is  2×3=6(for  least case) thats what they given the least number divisible by both 3 and 5 is 15 for 2 digit num

manisha 10/6/2014 3:14:02 PM

plz explain 1 line

 

Manish chaturvedi 10/10/2014 10:39:16 AM

two digit no start from 10 to 99 so total no is 90.

how many no divisible by 3? [90/3=30 no]

how many no divisible by 5? [90/5=18 no]

how many no divisible by LCM of 3 and 5(15)? [90/15=6 no] this is a common no divisible by 3 and 5

a no divisible by 3  but not 5 is     30 - 6=24 numbers(only divide by 3 )

so probability is 24/90=4/15Ans

 

lavanya 11/2/2014 8:21:48 AM

toal two digit numbers=90

total two digit numbers multilple of 3 is starts from 12, 15, 18,21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.(30)

Which are multiple of 5 is 15, 30, 45, 60, 75, 90(6)

Question asked is the numbers which are multiple of 3 and not multiple of 5 is= 30-6= 24

total two digit numbers=90

therefore probability=24/90

 

Kuldip 11/19/2014 1:45:34 AM

@Manish & @lavanya

very nic explain

thanks

Dhananjay Singh 1/9/2015 3:39:56 PM

Hey, 

       as i solve this question that two digit no. from 10-99 are (99-10)+1=90. out of 90, divisible by 3 no. are 90/3=30. out this(30) total no. that divisible by 5 is 30/5=6(which are divisible by both 3 & 5).

but as mention in question find that no. which only divided by 3 & not by 5, so out of 30(all divisible by 3, some divisible by 5).

so, 30(all divisible by 3, some divisible by 5)-6(divisible by 3 & 5 both)=24(only divisible by 3 and not by 5).

24 out of 90=24/90=> 4/15 Ans.....

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