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- Question
476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:
Options- A. 6 and 2
- B. 8 and 2
- C. 6 and 5
- D. 8 and 5
- Correct Answer
- 8 and 5
ExplanationLet the number be 476ab0
476ab0 is divisible by 3
=> 4 + 7 + 6 + a + b + 0 is divisible by 3
=> 17 + a + b is divisible by 3 ------------------------(i)
476ab0 is divisible by 11
[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11
=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)
Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.
if a=6 and b=2,
17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer
if a=8 and b=2,
17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)
[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer
if a=6 and b=5,
17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer
if a=8 and b=5,
17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1
[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2
Since these values satisfies both equation 1 and equation 2, this is the answer
- 1. A alone can finish a work in 10 days and B alone can do it in 15 days. If they work together and finish it, then out of a total wages of Rs. 75, A will get?
Options- A. Rs. 30
- B. Rs. 37.50
- C. Rs. 45
- D. Rs. 50 Discuss
- 2. Suppose you can travel from a place A to a place B by 3 buses, from place B to place C by 4 buses, from place C to place D by 2 buses and from place D to place E by 3 buses. In how many ways can you travel ?from A to E?
Options- A. 36
- B. 64
- C. 74
- D. 72 Discuss
- 3. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Options- A. 11670
- B. 12000
- C. 11760
- D. 20050 Discuss
- 4. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Options- A. 120960
- B. 120000
- C. 146700
- D. None of these Discuss
- 5. If factory A turns out x cars an hour and factory B turns out y cars every 2 hours, the number of cars which both factories turn out in 8 hours is?
Options- A. 8(x + y)
- B. (8x +y)/2
- C. 16(x + y)
- D. (2x + y)4 Discuss
- 6. Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct
Options- A. 65000
- B. 64000
- C. 72000
- D. 36000 Discuss
- 7. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
Options- A. 4!/2!
- B. 3!/2!
- C. (4! x 3!) / 2!
- D. 36 Discuss
- 8. In how many ways can the letters of the word "PROBLEM" be rearranged to make 7 letter words such that none of the letters repeat?
Options- A. 49
- B. 7!
- C. 7^7
- D. 7^3 Discuss
- 9. A is twice as good a workman as B and together they finish a piece of work in 14 days. A alone can finish the work in?
Options- A. 11 days
- B. 21 days
- C. 28 days
- D. 42 days Discuss
- 10. There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference. If the members of the club decide to send two juniors and two seniors, how many different groupings are possible ?
Options- A. 23024
- B. 24023
- C. 23023
- D. 25690 Discuss
More questions
Correct Answer: Rs. 45
Explanation:
Since a alone can finish a work in 10 days and B alone can do it in 15 days. So if they work together then the ration of work done by A and B is = (1/10) : (1/15).
? The wages A will get = (1/10)[(1/10) + (1/15)] x 75
= Rs. 45
Correct Answer: 72
Explanation:
The bus fromA to B can be selected in 3 ways.
The bus from B to C can be selected in 4 ways.
The bus from C toD can be selected in 2 ways.
The bus fromD to E can be selected in 3 ways.
So, by the General Counting Principle, one can travel fromA to E in 3 x 4 x 2 x 3 ways = 72
Correct Answer: 11760
Explanation:
Required number of ways= = ( )= 11760.
Correct Answer: 120960
Explanation:
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8!/(2! x 2!)= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =4!/2!= 12.
Required number of words = (10080 x 12) = 120960
Correct Answer: (2x + y)4
Explanation:
? Factory A turns out x cars in one hour. Factory B turns out y/2 cars in one hour.
? In one hour both the factories A and B can turn out (x + y/2) cars
? In 8 hours both factories turn out = 8( x + y/2) cars
= 4(2x + y) cars.
Correct Answer: 65000
Explanation:
Out of 26 alphabets two distinct letters can be chosen in ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways.
Combined with letters there are X 100 ways = 65000 ways to choose vehicle numbers.
Correct Answer: (4! x 3!) / 2!
Explanation:
ABACUS is a 6 letter word with 3 of the letters being vowels.
If the 3 vowels have to appear together, then there will 3 other consonants and a set of 3 vowels together.
These 4 elements can be rearranged in 4! Ways.
The 3 vowels can rearrange amongst themselves in 3!/2! ways as "a" appears twice.
Hence, the total number of rearrangements in which the vowels appear together are (4! x 3!)/2!
Correct Answer: 7!
Explanation:
There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! ways.
Correct Answer: 21 days
Explanation:
(A's 1 day's work) : (B's 1 day's work) = 2 : 1
Now, ? (A + B)'s day's work = 1/14
? A's 1 day's work = (1/14) x 2/3 = 1/21
? A alone can finish the work in 21 days.
[Dividing 1/14 in the ratio 2 : 1 ]
Correct Answer: 23023
Explanation:
Choose 2 juniors and 2 seniors.
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