Quant Quiz On H.C.F. And L.C.M.

Dear reader here we are providing some question on H.C.F. and L.C.M which can be useful in your upcoming  exam.

           

1.    Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

      A.   4         

      B.   7

      C.  9         

      D.  13

2.    The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

      A.   276     

      B.   299

      C.  322     

      D.  345

3.    Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

      A.   4         

      B.   10

      C.  15       

      D.  16

4.    Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

      A.   4         

      B.   5

      C.  6         

      D.  8

5.    The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

      A.   9000   

      B.   9400

      C.  9600   

      D.  9800

6.    The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

      A.   101     

      B.   107

      C.  111     

      D.  185

7.    Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:

      A.   40       

      B.   80

      C.  120     

      D.  200

8.    The G.C.D. of 1.08, 0.36 and 0.9 is:

      A.   0.03    

      B.   0.9

      C.  0.18    

      D.  0.108

9.    The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

      A.   1         

      B.   2

      C.  3         

      D.  4

10.  The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

      A.   74       

      B.   94

      C.  184     

      D.  364

ANSWERS WITH EXPLANATION:

1.    (A)

      Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)

     = H.C.F. of 48, 92 and 140 = 4.

2.    (C)

      Clearly, the numbers are (23 x 13) and (23 x 14).

      Larger number = (23 x 14) = 322.

3.    (D)

      L.C.M. of 2, 4, 6, 8, 10, 12 is 120.

      So, the bells will toll together after every 120 seconds (2 minutes).

      In 30 minutes, they will toll together          (30/2) + 1 = 16 times.

4.    (A)

      N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)

        = H.C.F. of 3360, 2240 and 5600 = 1120.

      Sum of digits in N = (1 + 1 + 2 + 0) = 4

5.    (C)

      Greatest number of 4-digits is 9999.

      L.C.M. of 15, 25, 40 and 75 is 600.

      On dividing 9999 by 600, the remainder is 399.

      Required number (9999 - 399) = 9600.

6.    (C)

      Let the numbers be 37a and 37b.

      Then, 37a x 37b = 4107,

      ab = 3.

      Now, co-primes with product 3 are (1, 3).

      So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).

      Greater number = 111.

7.    (A)

      Let the numbers be 3x, 4x and 5x.

      Then, their L.C.M. = 60x.

      So, 60x = 2400 or x = 40.

      The numbers are (3 x 40), (4 x 40) and (5 x 40).

      Hence, required H.C.F. = 40.

8.    (C)

      Given numbers are 1.08, 0.36 and 0.90.   H.C.F. of 108, 36 and 90 is 18,

       H.C.F. of given numbers = 0.18.

9.    (B)

      Let the numbers 13a and 13b.

      Then, 13a x 13b = 2028

       ab = 12.

      Now, the co-primes with product 12 are (1, 12) and (3, 4).

10.  (D)

      L.C.M. of 6, 9, 15 and 18 is 90.

      Let required number be 90k + 4, which is multiple of 7.

      Least value of k for which (90k + 4) is divisible by 7 is k = 4.

       Required number = (90 x 4) + 4   = 364.

       

Read more ...

Quant Quiz For SSC

Dear reader here we are providing some question on profit and loss which can be useful in your upcoming SSC exam.

1.    What profit/loss percent did Ravi earn if he purchased an item of Rs.5,600 and sold it at three-fourth of its cost price?

      (a) Loss of 20 percent

      (b) Gain of 25 percent

      (c) Neither gain or loss

      (d) None of these

2.    The owner of a cell phone shop charges his customer 23% more than the cost price. If a customer paid Rs.7, 011 for a cell phone, then what was the cost price of the cell phone?

       (a) Rs.5, 845

       (b) Rs.6, 750

       (c) Rs.5, 900

       (d) None of these

3.    The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages.

      (a) 30%   

      (b) 32.50%  

      (c) 331/3%  

      (d) 40%  

     

4.    Raju purchased an item for Rs.4,500 and sold it at the gain of 15%. From that amount he purchased another item and sold it  at the loss of 10%. What is his overall gain/loss?

      (a) Gain of Rs.151.50   

      (b) Gain of Rs.157.50  

      (c) Loss of Rs.165

      (d) neither gain nor loss  

5.    A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?

      (a) 18%  

      (b) 15%  

      (c) 20%   

      (d) None of these

6.    Profit earned by an organization is distributed among officers and clerks in the ratio of 5:3 respectively. If the number of officers is 45 and the number of clerks is 80 and the amount received by each officer is Rs.25,000/-, what was the total amount of profit earned?

      (a) Rs.22 lakhs   

      (b) Rs.18.25 lakhs 

      (c) Rs.18 lakhs  

      (d) Rs.23.25 lakhs  

7.    The cost of 8 gel pens and 12 ball pens is Rs.82. What would be the cost of 36 gel pens and 54 ball pens?

      (a) Rs.366  

      (b) Rs.365  

      (c) Rs.369  

      (d) Rs.364   

8.    A merchant sells his two cars – one at 15% loss and another at 12% profit. If the cost prices of the two cars are in the ratio of 1:2, what is his percent profit or loss?

      (a) 3% profit    

      (b) 2% loss  

      (c) 2% profit   

      (d) 1.2%loss   

9.    The profit earned after selling an article for Rs.675 is twice the loss incurred after selling the article for Rs.435. What is the cost price of the article?

      (a) Rs.450  

      (b) Rs.595  

      (c) Rs.400  

      (d) Rs.515  

10.  Mohan purchased 15 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Wheat is the total amount that he paid to the shopkeeper?

      (a) Rs.598    

      (b) Rs.594  

      (c) Rs.596    

      (d) Rs. 595   

ANSWERS WITH SOLUTION:

1. (d):

       C.P. = Rs.5600

      S.P. = Rs.5600x ¾ = Rs.4200

      Loss = Rs.5600-4200 = Rs.1400

      Loss percentage = 1400x100/5600 = 25%.

2. (d):

      123% of CP =SP

      Therefore, CP = Rs.7,011x100/123 = Rs.5700.

3. (c):

      The gain is 4 out of 12 articles.

      Therefore, gain percentage = 4x100/12 = 100/3 = 331/3%.

4. (b):

      1^st SP = Rs.4500 + 15% of 4500 = Rs.4500+Rs.675 = Rs.5175

      2^nd CP = Rs.5175.

      2^nd SP = Rs.5175 – 10% of 5175 = Rs.4657.50

      Overall gain = Rs.4657.50 – 4500 = Rs.157.50.

5. (d):

      Let the CP of the article = Rs.100.

      Then labeled price = Rs.130.

      SP   = Rs.130- 10% of 130 = Rs.130-13 = Rs.117.

      Gain = Rs.117 – Rs.100 = Rs.17.

      Therefore, gain/profit percent = 17%.

6. (c):

      The total amount distributed among 45 officers = Rs.45x25000 = Rs.1125000.

      Let the amount distributed to 80 clerks be ‘x’.

      Then   1125000/x = 5/3, therefore, x = Rs.675000.

      Therfore, the Total profit = Rs.1125000 + 675000 = Rs.18 lakhs.

7. (c):

      From the given statement we have,

      The cost of 4 gel pens + 6 ball pens = Rs.41.

      Multiplying each terms by 9, we get

      The cost of 36 gel pens + 54 ball pens = Rs.369.

8. (a):

      Given that CPs are in the ratio 1:2

      Therefore let the CPs be Rs.100 & Rs.200 respectively,

      1^st SP = 100-15% of 100 = Rs.86.

      2^nd SP = 200 + 12% of 200 = Rs.224.

      Total CP = Rs.300.  Total SP = 85+224 = Rs.309.

      Profit = Rs.309-300 = Rs.9.

      Profit percent = 9x100/300 = 3% profit.

9. (d):

      Let ‘x’ be the CP of the article.

      i.e. Rs.675-x = 2(x-435)

      675-x = 2x-870

      675+870 = 3x, therefore, x=1545/3  =Rs.515.

10. (a):

      Price of 15 kgs of rice at Rs.26/kg = 15x26 = Rs.390

      Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208

      Therefore, Total amount = Rs.390+Rs.208 = Rs.598.

Read more ...