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Numbers Exercise 3

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Numbers 3

  • This online quiz will test your knowledge of Numbers in Quantitative Aptitude.
  • This Online Test is useful for academic and competitive exams.
  • Multiple answer choices are given for each question in this test. You have to choose the best option.
  • After completing the test, you can see your result.
  • There is no negative marking for wrong answers.
  • There is no specified time to complete this test.

If (74)² is subtracted from the square of a number, the answer so obtained is 5340. What is the number?

Let the number be x.

Then, x² – (74)² = 5340

⇒ x² = 5340 + 5476 = 10816

⇒ x = number-system-q-49203.png

If (74)² is subtracted from the square of a number, the answer so obtained is 3740. What is the number?

Let the number be = x

According to the question

x² – (74)² = 3740

⇒ x² = 3740 + 5476 = 9216

∴ x = number-system-q-49194.png = 96

If (46)² is subtracted from the square of a number, the answer so obtained is 485. What is the number?

Let the number be x

∴ x² – (46)² = 485

⇒ x² = 485 + (46)² = 2601

∴ x = number-system-q-49185.png = 51

If (57)² is added to the square of a number, the answer so obtained is 8010. What is the number?

Let the number be = x

According to the question,

x² + 57² = 8010

⇒ x² + 3249 = 8010

⇒ x² = 8010 – 3249 = 4761

⇒ x = number-system-q-49175.png = 69

If (9)³ is subtracted from the square of a number, the answer so obtained is 567. What is the number?

Let the required number be x

∴ x² – (9)³ = 567

x² = 567 + 729 = 1296

∴ x = number-system-q-49167.png = 36

If (78)² is subtracted from the square of the number, the answer so obtained is 6,460. What is the number?

Let the number be x.

According to the question,

x² – 78² = 6460

⇒ x² = 6460 + 6084

⇒ x² = 12544

What is the least number to be added to 4400 to make it a perfect square?

number-system-q-49157.png = 66.33

∴ Required number = 67² – 4400

= 4489 – 4400 = 89

⇒ x = number-system-q-49148.png = 112

Which least number shall be added to 8115 to make it a perfect square?

number-system-q-49142.png

∴ required number = 91 × 91 – 8115 = 166

What is the least number to be added to 4321 to make it a perfect square?

number-system-q-49135.png

∴ (66)² – 4321 = 4356 – 4321 = 35

What is the least number to be added to 4700 to make it a perfect square?

69 × 69 = 4761

68 × 68 = 4624

Clearly, 4624 < 4700 < 4761

∴ Hence, 61 should be added to make = 4761 – 4700 = 61

What is the least number to be added to 3986 to make it a perfect square?

number-system-q-49129.png = 63.13

∴ Here, 63² = (64)² – 3986

= 4096 – 3986 = 110

What is the least number to be added to 1500 to make it a perfect square?

38² = 1444

39² = 1521

∴ Required number

= 1521 – 1500 = 21

The difference between two numbers is 3 and the difference between their squares is 63. Which is the larger number?

Let the larger and smaller numbers be x and y respectively.

Then, x – y = 3 ...(i)

and, x² – y² = 63

⇒ (x + y) (x – y) = 63

⇒ number-system-q-47974.png ...(ii)

From equation (i) and (ii),

x = 12

If (12)³ is subtracted from the square of a number the answer so obtained is 976. What is the number?

Let the number be x.

x² - (12)3 = 976

∴ x² = 976 + 1728 = 2704

∴ x = number-system-q-47968.png

If (56)² is added to the square of a number, the answer so obtained is 4985. What is the number?

Let the number be x.

x² + (56)² = 4985

⇒ x² = 4985 – 3136 = 1849

∴ x = number-system-q-47962.png= 43

The difference between a two-digit number and the number obtained by interchanging the two digits of the number is 9. The sum of the digits of the number is 15. What is the product of the two digits of the two-digit number?

Let the two-digit number be

= 10 x + y, where x < y.

Number obtained after interchanging the digits = 10 y + x

According to the question,

10 y + x – 10 x – y = 9

⇒ 9y – 9x = 9

⇒ 9(y –x) = 9

⇒ y – x = 1 ...(i)

and x + y = 15 ...(ii)

From equations (i) and (ii),

y = 8 and x = 7

∴ Required product = 8 × 7 = 56

The number obtained by interchanging the two digits of a two-digit number is less than the original number by 18. The sum of the two digits of the number is 16. What is the original number?

Let the number be (10x + y)

Then, (10x + y) – (10y + x) = 18

⇒ 9x – 9y = 18

⇒ x – y = 2 ...(i)

and, x + y = 16 ...(ii)

∴ x = 9, y = 7

From equations (i) and (ii),

So, the number is (10 × 9 + 7) = 97

How many numbers from 1 to 100 are there each of which is not only exactly divisible by 4 but also has 4 as a digit?

The numbers from 1 to 100 which are exactly divisible by

4 are 4, 8, 12, 16, 20,24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100.

But each number should have 4 as its digit.

The required numbers are 4, 24, 40, 44, 48, 64, 84.

Clearly, there are 7 such numbers.

The numbers 1 to 29 are written side by side as follows 1234567891011 ... 2829. If the number is divided by 9, then what is the remainder?

Sum of the digits of the ‘super’ number

= 1 + 2 + 3 +.... + 29

number-system-q-49353.png

number-system-q-49347.png

= number-system-q-49340.png

Now, sum of digits in the number 435 = 4 + 3 + 5 = 12 which gives a remainder of 3 when divided by 9.

If x959y is divisible by 44 and y >5, then what are values of the digit x and y?

Here 44 = 11 × 4

∴ the number must be divisible by 4 and 11 respectively. Test of 4 says that 9y must be divisible by 4 and since y > 5, so y = 6

Again , x 9596 is divisible by 11,

so x + 5 + 6 = 9 + 9

⇒ x = 7

Thus x = 7, y = 6

The quotient arising from the division of 24162 by a certain number x is 89 and the remainder is 43. Find x.

24162 = 89x + 43

⇒ x = (24162 – 43) ÷ 89 = 271

Find the unit’s digit in the product (2467)¹⁵³ × (341)⁷².

Clearly, unit’s digit in the given product = unit’s digit in 7¹⁵³ × 1⁷².

Now, 7⁴ gives unit digit 1.

∴ 7¹⁵³ gives unit digit (1 × 7) = 7. Also 1⁷² gives unit digit 1.

Hence, unit’s digit in the product

= (7 × 1) = 7.

The unit’s digit in the product (7⁷¹×6⁵⁹×3⁶⁵) is:

Unit digit in 7⁴ is 1.

Unit digit in 7⁶⁸ is 1.

∴ Unit digit in 7⁷¹ = 1 × 7³ = 3

Again, every power of 6 will give unit digit 6.

∴ Unit digit in 6⁵⁹ is 6.

Unit digit in 3⁴ is 1.

∴ Unit digit in 3⁶⁴ is 1.

Unit digit in 3⁶⁵ is 3.

∴ Unit digit in (7⁷¹ × 6⁵⁹ × 3⁶⁵)

= Unit digit in (3 × 6 × 3) = 4.

How many times must 79 be subtracted from 5 × 10⁴ so as to obtain 43759?

Let x be the number of times, then

79x + 43759 = 50,000

⇒ x = (50000 – 43759) ÷ 79 = 79

55³ + 17³ - 72³ is divisible by

number-system-q-49334.png

number-system-q-49328.png

number-system-q-49322.png

number-system-q-49316.png

The digit in the unit’s place of the number represented by (7⁹⁵ – 3⁵⁸) is:

Unit digit in 7⁴ is 1. So, unit digit in 7⁹² is 1.

∴ Unit digit in 7⁹⁵ is 3.

Unit digit in 3⁴ is 1.

∴ Unit digit in 3⁵⁶ is 1.

∴ Unit digit in 3⁵⁸ is 9.

∴ Unit digit in (7⁹⁵ – 3⁵⁸) = (13 – 9) = 4.

What is the digit in the unit place of 2⁵¹?

The digit in the unit’s place of 2⁵¹ is equal to the remainder when 2⁵¹ is divided by 10. 2⁵ = 32 leaves the remainder 2 when divided by 10. Then 2⁵⁰ = (2⁵)¹⁰ leaves the remainder 2¹⁰ = (2⁵)² which in turn leaves the remainder 2² = 4. Then
2⁵¹ = 2⁵⁰×2, when divided by 10, leaves the remainder 4×2 = 8.

Now check your Result..

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