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Problems on Numbers
1.If one-third of one-fourth of a number is 15, then three-tenth of that number is:

Answer:Option 1

Explanation:

Solution:
LetthenumberbexThen,13of14ofx=15x=15×15=180So,requirednumber=(310×180)=54

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2.Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

Answer:Option 1

Explanation:

Solution:
Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3    ⇔    x = 11.
∴ Third integer = x + 4 = 15.

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3.The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

Answer:Option 1

Explanation:

Solution:
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
⇒ 9(x - y) = 36
x - y = 4.

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4.A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

Answer:Option 1

Explanation:

Solution:
Lettheten'sandunitdigitbexand8xrespectivelyThen,(10x+8x)+18=10×8x+x10x2+8+18x=80+x29x2+18x72=0x2+2x8=0(x+4)(x2)=0x=2

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5.The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

Answer:Option 1

Explanation:

Solution:
Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x - y = 3   or   y - x = 3.
Solving x + y = 15   and   x - y = 3, we get: x = 9, y = 6.
Solving x + y = 15   and   y - x = 3, we get: x = 6, y = 9.
So, the number is either 96 or 69.
Hence, the number cannot be determined.

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6.The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

Answer:Option 1

Explanation:

Solution:
Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
⇒ (a + b + c) = √400 = 20.

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7.A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

Answer:Option 1

Explanation:

Solution:
Let the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
∴ (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

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8.Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

Answer:Option 1

Explanation:

Solution:
LetthenumberbexThen,x+17=60xx2+17x60=0(x+20)(x3)=0x=3

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9.The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

Answer:Option 1

Explanation:

Solution:
LetthenumberbexandyThen,xy=9375andxy=15xy(x/y)=937515y2=625y=25x=15y=(15×25)=375Sumofthenumber=x+y=375+25=400

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10.The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

Answer:Option 1

Explanation:

Solution:
Let the numbers be x and y.
Then, xy = 120 and x2 + y2 = 289.
∴ (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
x + y = √529 = 23.

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