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- Question
- A number is greater than the square of 44 but smaller than the square of 45. If one part of the number is the square of 6 and the number is a multiple of 5, then find the number.?
Options- A. 1940
- B. 2080
- C. 1980
- D. Cannot be determined
- Correct Answer
- 1980
ExplanationLet the number be x.
442 < x < 452
? 1936 < x < 2025 ...(i)
From equation (i), the required number will be any number between 1936 and 2025. Since one part of the number is the square of 6 means one factor is 36.
? L, C, M of 36 and 5 = 180
? Number will be multiple of 180 i,e.,
180 x 11 = 1980 the only value which satisfies the equation (i). - 1. The difference between two number is 18 if four times the second number is less then three what is the sum these two number?
Options- A. 100
- B. 80
- C. 86
- D. 92 Discuss
- 2. Find the maximum number of tree which can plant 20 m apart on the two side of straight road 1760 m long
Options- A. 174
- B. 176
- C. 180
- D. 178 Discuss
- 3. Out of three given number the first number is twice the second and thrice number is 154 then what is the difference between the first and third number?
Options- A. 126
- B. 42
- C. 168
- D. 52 Discuss
- 4. The sum of the two position number P and Q is 2.5 time their difference .If the product of the number 84 then the what is the sum of those two number?
Options- A. 26
- B. 24
- C. 22
- D. 20 Discuss
- 5. On children day sweet were to be equally distributed among 300 children. But on that particular day 50 children remain absent hence each child got one extra sweet. How many sweet were distributed?
Options- A. 1450
- B. 1700
- C. 1500
- D. 1650 Discuss
- 6. When a certain number is multiplied by 13, the product consists entirely of fives. The smallest such number is?
Options- A. 41625
- B. 42515
- C. 42735
- D. 42135 Discuss
- 7. A number consist of two digit whose sum is 10 If the digit of the number are reversed then the number decreased by 36. Which of the following is correct.
I. The number is divisible by a composite number.
II. The number is a multiple of a prime number.
Options- A. only I
- B. only II
- C. Both I and II
- D. Neither I nor II Discuss
- 8. Every prime number of the form 3k + 1 can be represented in the form 6m + 1 (where k, m are integers), When
Options- A. k is odd
- B. k is even
- C. k can be both odd and even
- D. No such from is possible Discuss
- 9. A number consist of two digit whose sum is 10. If the digits of the number are reversed, then the number decreased by 36. Which of the following is/are correct?
I. The number is divisible by a composite number.
II. The number is multiple of a prime number.
Options- A. Only I
- B. Only II
- C. Both I and II
- D. neither I nor II Discuss
- 10. If the numerator of a certain fraction is increased by 2 and the denominator is increased by 1, then the resulting fraction is equal to the 1/2. If how ever the numerator is increased by 1, then denominator is decreased by 2, then the resulting fraction is equal to 3/5. Find the original fraction?
Options- A. 2/7
- B. 3/5
- C. 1/7
- D. 2/5 Discuss
Number System problems
Search Results
Correct Answer: 92
Explanation:
Let first number = P
And second number = Q
According to the question
P - Q = 10 ....(i)
And 3P - 4Q = 18...(ii)
on multiply eq (i) by 3 and then subtract eq (ii) from it
3P - 3Q = 54
3P - 4Q = 18
Q = 36
On putting the value of Q in the eq (i)
P = 18 + Q = 18 +36
? P = 54
Required sum = P + Q = 54 +36 =90
Correct Answer: 178
Explanation:
Number of trees that can be planted on one side of road = (1760 / 20) + 1
= 88 + 1
=89
? Trees on the both side = 2 x 89=178
Correct Answer: 168
Explanation:
Let the third number = N
Then the first number = 3N
And second number = 3N/2
According to the question [N + 3N + 3N/2] / 3=154
? (2N +6N +3N) / 6 = 154
? N = (154 x 6) / 11 = 84
? Required difference = 3N - N = 2N
= 2 x 84 = 168
Correct Answer: 20
Explanation:
Let the number be P and Q
According to the question
(P + Q) = 2.5 (P - Q)
? P + Q = 2.5P - 25Q
? 3.5Q = 1.5P
? P / Q = 7/3 .....(i)
Now PQ = 84
? Q2 = (84 x 3) / 7
? Q2 = 36
? Q = 6
&ther4; P = (7/3) x 6 = 14
Sum of the number = P + Q = 14 + 6 = 20
Correct Answer: 1500
Explanation:
let the total number of sweet = N
According to the question
(N/250) - (N/300) = 1
? (6N - 5N) / 1500=1
? N = 1500
Correct Answer: 42735
Explanation:
By trial, we find that the smallest number consisting entirely of fives and exactly divisible by 13 is 555555. On dividing 555555 by 13, we get 42735 as quotient.
? Req. smallest number =42735.
Correct Answer: only II
Explanation:
let the two-digit number be 10p + q
Now according to the question
p + q = 10
and (p +10q) + 36 = (q + 10p)
? -9q + 9p = 36
? -q + p = 4 ....(ii)
on adding eq (i) and (ii) we get
2p = 14 ? p =7
? p = 7 and q = 4
? Required number is the 73
So, the number is a multiple of prime number.
Correct Answer: k is even
Explanation:
The only one even prime number is 2 and this is not in the form of 3k + 1.
Thus any prime number of the form 3k + 1 is an odd number.
This means 3k must be even number which implies that k must be even number also.
Let k = 2m.
Then a prime of the form 3k + 1 is of the form 3(2m) + 1 = 6m+1.
Every prime number of form 3k + 1 can be represented in the form 6m + 1 only, when k is even.
Correct Answer: Only II
Explanation:
Let the two digit number be 10x + y.
Now, according to the question,
x + y = 10............(i)
if digits reversed , number get decreased by 36,
and ( x +10y) = ( 10x + y ) - 36
? - 9y + 9x = 36
? x - y = 4 ..................... (ii)
On adding Eqs. (i) and (ii), we get
2x = 14
? x = 7
? x = 7 and y = 3
? Required number is 73.
So,the number is a multiple of a prime number.
Correct Answer: 2/7
Explanation:
Let the fraction be x / y.
According to the question,
( x+2)/(y+1) = 1/2
? 2x + 4 = y+1
? 2x - y = -3 .........................(i)
Again according to the question,
(x+1)/(y-2) = 3/5
? 5x +5 = 3y - 6
? 5x - 3y = -11..........................(ii)
on multiplying Eq. (i) by 3 and then subtracting from Eq. (ii) we get,
multiplying Eq. (i) by 3
6x - 3y = -9
subtracting from Eq. (ii)
5x- 3y - ( 6x - 3y ) = -11 - (-9)
5x- 3y - 6x + 3y = -11 + 9
- x = - 2
x= 2
On putting the value of x in Eq. (i) we get
2x- y = -3
2 x 2 - y = -3
? 2 x 2 -y = -3
? -y = -3 - 4
? y = 7
? Original fraction = x/y =2/7
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