Mathmetics

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

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Q1.
The sum of two numbers is 27 and their H.C.F is 3. If one of the number is lies between  13 to 16, the find the value of the other number ?
1) 12 2) 15
3) 18 4) 24
5)None of these
Answer : 12
Explanation : Let, two numbers are 3x and 3y respectively.
Then, 3x + 3y = 27  
 or 3 (x + y) = 27
or (x + y) = 27/3 = 9
So, pairs of numbers are  9 = (1,8) , (2,7) , ( 3,6) and  (4,5) .
Thus the numbers are 3 x 4 = 12 and 3 x 5 =15 
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Q2.
What is four-digit largest number which when divided by 4, 5 , 6, 8 and 12 leaves reminder is  zero in each case ? 
1) 9936 2) 9950
3) 9960 4) 9990
5)None of these
Answer : 9960
Explanation : The L.C.M of 4, 5 , 6, 8 and 12  is 120. 
The four-digit largest number is 9999.
Then, if 9999 is divided by 120, reminder is 39.
So, the require number = 9999 - 39 = 9960.
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Q3.
A rectangular size floor has 240 feet length and 200 feet wide. How many largest square size marbels slabs are require to pave ,so that no waste of slabs in the paving ?
1) 24 2) 25
3) 30 4) 36
5)None of these
Answer : 30
Explanation : The H.C.F of 240 and 200 is 40.
Area of the floor = (240 X 200) square feet and area of the slab is (40X40) square feet.
So, Numbers of slabs require = (240 X 200)/(40X40) = 30.

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Q4.
A worker has paid Rs.4320 if he works for all day but he has paid Rs.2520 due to some days of absent in a month.How many days he was absent ?
1) 2 days 2) 3 days
3) 4 days 4) 5 days
5)None of these
Answer : 5 days
Explanation : The H.C.F of 4320 and 2520 is 360.
So, 4320/360 = 12 days and 2520/360 = 7 days
Thus, numbers of he absent =12-7=5 days.
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Q5.
The H.C.F and L.C.M of two numbers are 13 and 455 respectively. If one of the numbers lies between 75 and 125, then what is that number ?
1) 78 2) 91
3) 104 4) 117
5)None of these
Answer : 91
Explanation : Let, two numbers are 13x and 13y respectively.
So, 13x X 13y  = 13 X 455
or xy = 35
 Then, pairs  of numbers are 35 = (1 X 35) , (5 x 7).
So, second pairs is considerable i.e. 13X5 = 65 and 13 X 7 = 91 

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Q6.
The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then what is their difference ? 
1) 10 2) 12
3) 15 4) 20
5)None of these
Answer : 10
Explanation : Let, two numbers are 5x and 5y respectively. 
So, 5x X 5y = 5 X 495
or 25xy = 5 X 495 
or xy = 99
So, pairs of numbers are  i.e. 99 = (1 X 99)  and (9 x 11)
Therefore , the satisfy numbers are 9 x 5 = 45 and 11 x 5 = 55
So, the difference is 55 - 45 = 10. 

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Q7.
The L.C.M of two numbers is 45 times their H.C.F. If one of the number is 125 and the sum of H.C.F and L.C.M is 1150, the other number is - 
1) 215 2) 220
3) 225 4) 235
5)None of these
Answer : 225
Explanation : Given that, 45 H.C.F = L.C.M   and  
H.C.F + L.C.M = 1150 
or H.C.F + 45 H.C.F = 1150
or 46 H.C.F = 1150
or H.C.F = 1150/46 =25
So, L.C.M = 25 X 45 = 1125
Now, we can get 125 X x = 25 X 1125
or   x =  (25 X 1125) /125 = 225

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Q8.
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
1) 196 2) 630
3) 1260 4) 2520
5)None of these
Answer : 630
Explanation :
L.C.M. of 12, 18, 21 30                
     = 1260.      
So, required number = (1260 รท 2)   = 630.
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Q9.
What is the least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder ?
1) 1677 2) 1683
3) 2523 4) 3363
5)None of these
Answer : 1683
Explanation :
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
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Q10.
The sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively. What should be the sum of the reciprocals of the numbers ?
1) 55/601 2) 12/55
3) 11/120 4) 11/112
5)None of these
Answer : 11/120
Explanation :
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