General Mathematics

Question: The H.C.F of 3556 and 3444 is :
A25

B26

C28

D23

Note: solution:
3444)    3556   (1 
             3444   
            --------
             112)      3444    (30
                          3360
                        ----------
                             84)   112   (1
                                       84
                                    --------
                                        28)    84   (3
                                                 84
                                               -------
                                                 `xx`

    `:.`H.C.F.=28

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Question: The H.C.F. of 210, 385 and 735 is :
A7

B14

C21

D35

Note: solution:
210=`2 xx 3 xx 5 xx 7`, 385=`5 xx 7 xx 11` & 735=`3 xx 5 xx 7^2`.

`:.`H.C.F.=`5 xx 7`=35.

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Question: Which of the following is a pair of co-primes ?
A(21, 35)

B(23, 92)

C(18, 25)

D(16, 62)

Note: solution:
H.C.F.of 18 and 25 is 1. So, they are co-primes.

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Question: The H.C.F. of `2/3 ,8/9,64/81 and 10/27` is :
A`2/3`

B`2/81`

C`160/3`

D`63/700`

Note: solution:
H.C.F.=`text(H.C.F. of 2,8,64,10)/text(L.C.M. of 3,9,81,27)` =`2/81`.

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Question: The H.C.F. of `9/10`,`12/25`,`18/35`and `21/40` is :
A`3/5`

B`252/5`

C`3/1800`

D`63/700`

Note: solution
H.C.F. =`(H.C.F. of 9,12,18,21)/(L.C.M. of 10,25,35,40)`=`3/2800`

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Question: The L.C.M. of 26,56,104 and 182 is :
A546

B1274

C728

D784

Note: solution:
13 |  26 - 56 - 104 - 182
___|__________________________
 7 |   2  -56 -    8  -   14
___|___________________________
 2 |   2  - 8  -   8  -     2
___|___________________________
 4 |   1  - 4  -   4  -     1
___|___________________________
   |   1  - 1  -   1  -     1

    `:.`L.C.M.=(13`xx`7`xx`2`xx`4`xx`)=728.

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Question: The L.C.M. of 148 and 185 is :
A680

B740

C3700

D2960

Note: solution:
H.C.F. of 148 and 185 is 37.
  
L.C.M.=`((148xx185)/37)` =740.

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Question: A man buys oranges at  tk 5 a dozen and equal number at tk 4 a dozen. He sells them at tk 5.50 a dozen and make a profit of rs 50. How many oranges does he buy?
A30 Dozen

B40 Dozen

C50 Dozen

D60 Dozen

Note: C.P of 2 dozen oranges = Tk (5 + 4)
= 9 Tk
S.P of 2 dozen oranges = Tk 11
If profit is Tk 2, oranges bought = 2 dozen
If profit is Tk 50, oranges bought = `(2/2 xx 50)` dozen
= 50 dozen

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Question: If, by selling an article for tk.100, a man gains tk. 15, then his gain percent is?
A15%

B`12 2/3`%

C`17 11/17`%

D`17 1/4`%

Note: Here S.P = tk 100, 
Loss=Tk 15, 
So C.P=tk(100-15)
      =Tk 85,
therefore Gain % = `((15)/85xx100)`%=`17(11)/17` %

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Question: what is the loss percent if a man is loses tk 10 on selling an article for tk 100?
A`9 1/11`%

B10 %

C`11 1/9` %

DNone

Note: Here S.P = Tk 100, 
Loss=Tk 10, 
So C.P= `(100)/90 xx 100`
=Tk `(1000)/9`
therefore Loss % =`(10xx9/1000 xx100)`%
                     = 9 %

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