A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is
220030
22030
1220
1250
A.
220030
Divisor = 555 + 445 = 1000
Remainder = 30 (given)
Quotient = (555 - 445) x 2
= 110 x 2 = 220
Dividend = (Divisor x Quotient) + Remainder
= 1000 x 220 + 30 = 220030
The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4. If the denominator 7+C (C > -7) is a constant, then the minimum value of the fraction is
5
-5
D.
Let the first number be x.
then, second number would be (x+2).
According to the question,
x + 2 + 4 = 7 + c
⟹ x + 6 = 7 + c
⟹ x = 1 + c
∴ Fraction
For the minimum value,
- 3 < c < -1
∴ c = -2
∴ Required value of fraction = -1/5
On dividing a certain number by 342 we get 47 as remainder. If the same number is divided by 18, what will be the remainder?
15
11
17
13
B.
11
Shortcut Method:
Required remainder = Required remainder on dividing 47 by 18 = 11
When a number x is divided by a divisor it is seen that the divisor = 4 times the quotient = double the remainder. If the remainder is 80 then the value of x is
6480
9680
8460
4680
A.
6480
Divisor = 2 x remainder
= 2 x 80 = 160
Again,
4 x Quotient = 160
⟹ Quotient = 160 / 4 = 40
∴ x (Dividend) = Divisior x Quotient + Remainder
= 160 x 40 + 80 = 6480
The sum of three numbers is 2, the 1st number is 1/2 times the 2nd number and the 3rd number is 1/4 times the 2nd number. The 2nd number is
7/6
8/7
9/8
10/9
B.
8/7
Let the second number be x.
∴ First number = x/2
Third number = x/4
∴ x + x/2 + x/4 = 2
⟹ (4x + 2x + x)/4 = 2
⟹ 7x = 8 ⟹ x = 8/7
Three numbers are in Arithmetic Progression (AP) whose sum is 30 and the product is 910. Then the greatest number in the AP is
17
15
13
10
C.
13
Let three numbers in A.P. be a - d, a and a + d respectively.
According to the question,
(a - d) + (a) + (a + d) = 30
⇒ 3a = 30 ⇒ a = 30/3 = 10
Again, a (a - d) (a + d) = 910
⇒ 10 (10 - d) (10 + d) = 910
⇒ 100 - d^{2} = 91
⇒ d^{2} = 100 - 91 = 9
⇒
∴ Largest number = a + d = 10 + 3 = 13
The sum of three numbers is 252. If the first number is thrice and the second and third number is two-third of the first, then the second number is
41
21
42
84
C.
42
Let second number = x
∴ First number = 3x
Third number = (2/3). (3x) = 2x
According to the question,
3x + x + 2x = 252
⟹ 6x = 252
⟹ x = (252/6) = 42
Each member of a club contributes as much rupees and as much paise as the number of members of the club. If the total contribution is Rs. 2525, then the number of members of the club is
60
45
55
50
D.
50
Let Number of members in the club = x
According to the question,
The sum of three numbers is 252. If the first number is thrice the second and third number is two-third of the first, then the second number is
255
260
265
270
A.
255
Let the positive numbers be x, y and z (respectively).
∴ x^{2} + y^{2} + z^{2} = 323 ...(i)
and, x^{2} + y^{2} = 2z ...(ii)
∴ z^{2} + 2z = 323
⟹ z^{2} + 2z - 323 = 0
⟹ z^{2} + 19z - 17z - 323 = 0
⟹ z (z + 19) - 17 (z + 19) = 0
⟹ (z - 17) (z + 19) = 0
⟹ z = 17 because z ≠ - 19
∴ x^{2} + y^{2} = 2 x 17 = 34 = 3^{2} + 5^{2}
∴ xyz = 3 x 5 x 17 = 255
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