Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

Q201.
What is the total numbers of  3-digit numbers  which are completely divisible  by 6 ?
1) 140 2) 150
3) 152 4) 159
5)None of these
Answer : 150
Explanation :
The 3-digit number divisible by 6 are : 102, 108, 114,... , 996
It is an A.P. series where  a = 102, d = 6 and l = 996
Let, the number of terms be n. Then tn = 996.
or a + (n - 1) d = 996
or 102 + (n - 1) x 6 = 996
or 6 x (n - 1) = 894
or (n - 1) = 149
or n = 150
So, number of terms = 150.
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Q202.
Directions -: Study the following graph and table answer the questions given below. 

Number of tourists that visited seven different locations of India in the year 2011 (in thousands)


What is the percentage of the number of people visiting location G with respect to that visiting all other locations in the year 2011 ?
1) 6.25% 2) 8.15%
3) 10.05% 4) 11.36%
5)None of these
Answer : 6.25%
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Q203.
Directions -: Study the following graph and table answer the questions given below. 

Number of tourists that visited seven different locations of India in the year 2011 (in thousands)


What is the ratio of the number of females visiting B in the year 2011 to that visiting F in the same year ?
1) 1 : 1 2) 45 : 56
3) 47 : 56 4) 23 : 28
5)None of these
Answer : 45 : 56
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Q204.
If the number 653 xy is divisible by 90, then (x + y) = ?
1) 2 2) 3
3) 4 4) 6
5)None of these
Answer : 4
Explanation :
90 = 10 x 9
Clearly, 653xy is divisible by 10, so y = 0
Now, 653x0 is divisible by 9.
So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.
Hence, (x + y) = (4 + 0) = 4.
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Q205.
If n is a natural number, then (6n2 + 6n) is always divisible by: 
1) 6 only 2) 6 and 12 both
3) 12 only 4) by 18 only
5)None of these
Answer : 6 and 12 both
Explanation : (6n2 + 6n) = 6n (n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
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Q206.
What would be the unit digit of the following expressions.
(123)125 + (234) 127 = ?
1) 4 2) 6
3) 7 4) 9
5)None of these
Answer : 7
Explanation : We know that, any digit multiply four times, that product's unit digit will be same digit.
So,125/4 =31 quotient and 1 reminder and 127/4 = 31 divisor and 3 reminder.
Now, (123)1 + (234)3 = 3 + 4 = 7
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Q207.
A number, when divided by 135, the reminder is 45. If the same number is divided by 27, what would be the reminder ? 
1) 15 2) 18
3) 21 4) Data Inadequate
5)None of these
Answer : 18
Explanation : We know that, Dividend = (Divisor x Quotient) + Reminder.
So, Dividend = (135 x Quotient) + 45
Or Dividend = [ (27 x 5 x Quotient )+ (27 x 1 +18)]
When above Dividend is divided by 27, 18 will be reminder.

Short-Cut Method:

If the second divisor is a factor of the first divisor, then you just divide the second divisor with reminder.

i.e.   (R1/d2) = R2
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Q208.
There are some adult students in a class and their average age was 40 years. If 12 new students with an average age of 50 years join with them, their new average age will be increases by 5 years.What was the original strength of that class ? 
1) 8 2) 10
3) 12 4) 15
5)None of these
Answer : 12
Explanation : Let, there were x number of students in the class.
Given that their average age was 40 yrs.
So, their total age was = 40x yrs
Now, 12 new students join with them with an average age of 50 yrs.
Then, total age was = (12 x 50) = 600 yrs. and total students were x+12.
Now, new total age was = (4x + 600 ) yrs.
 So, (40x + 600 ) / (x+12) = 45
or 45x + 540 = 40x + 600
or 5x = 600 -540 = 60
or x = 60/5 = 12
Thus, original strength of that class was 12.
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Q209.
The average age of a class of 30 students is 12. If the teacher is also included the average becomes 13 years. Find the teacher's age.
1) 39 years 2) 40 years
3) 44 years 4) Data Inadequate
5)None of these
Answer : 39 years
Explanation :
When the teacher is included there are totally 31 members in the class and the average is increased by 1 year. This means that everyone got 1 extra year after distributing the extra years of the teacher.
So, extra years of the teacher are as follow: 31x1=31 years.
Age of the teacher = actual avg + extra years = 12 + 31 = 43 years 

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Q210.
10 man can finish a piece of work in 15 days. 8 women can finish the same work in 25 days. Only 10 women started working and in a few days completed a certain amount of work. After that 3 men joined them. The remaining work was completed by 10 women and 3 men together in 5 days . After how many did 3 men join with 10 women ?
1) 11 2) 13
3) 15 4) 10
5)None of these
Answer : 13
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