CAT Number properties & digits Questions

Integer-property questions use parity, signs, place values and digit restrictions. Translating a digit pattern into an algebraic expression can expose divisibility and size constraints.

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Key concepts

• Even and odd integers
• Place-value expressions
• Digit sums, reversal and bounds

CAT number properties & digits practice questions

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Common mistakes

• Allowing a leading zero in a number with a specified digit length.
• Assuming a pattern found in a few examples is a proof.

Practical solving approaches

• Represent digits explicitly with their allowed ranges.
• Use parity, divisibility and upper or lower bounds to reduce cases before enumeration.

Number properties & digits FAQs

How can I express a two-digit number algebraically?

If its tens digit is a and units digit is b, write it as 10a + b, with a from one to nine and b from zero to nine.

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CAT Number properties & digits Questions

Integer-property questions use parity, signs, place values and digit restrictions. Translating a digit pattern into an algebraic expression can expose divisibility and size constraints.

16 free practice questions

Key concepts

• Even and odd integers
• Place-value expressions
• Digit sums, reversal and bounds

CAT number properties & digits practice questions

Question 1Type in the answerEASY

Question 1

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

A two-digit number is the sum of the product of its digits and the sum of its digits. The units digit of the number is

Your answer

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Question 2Multiple choiceMEDIUM

Question 2

Select the correct alternative from the given choices.

If x = –0.5, then which of the following has the smallest value?

Choose an answer

A.

B.

C.

D.

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Question 3Type in the answerMEDIUM

Question 3

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Answer the questions independently of each other.

The smallest positive integer which can be expressed as a sum of two different cubes in two different ways is:

Your answer

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Question 4Multiple choiceMEDIUM

Question 4

Select the correct alternative from the given choices.

Answer the questions independently of each other.

When asked about their ages, Ram and Rohit said that their ages are odd integers and sum of square of their ages is 729. If Ram is older than Rohit, then find the age of Rohit.

Choose an answer

A.21 yearsB.23 yearsC.19 yearsD.Ram and Rohit are lying

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Question 5Multiple choiceHARD

Question 5

Select the correct alternative from the given choices.

Answer the questions independently of each other.

The set T contains all the numbers of the form (n + 2), (2n + 2), (3n + 2) and (4n + 2), where n is a natural number and takes values from 1 to 5. How many distinct prime numbers does T contain?

Choose an answer

A.2B.5C.12D.7

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Question 6Type in the answerMEDIUM

Question 6

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Refer to the data below and answer the questions that follow.

A maxi-power number is defined as a number which is a perfect square, cube, fourth power, fifth power, sixth power, seventh power, eighth power, ninth power and tenth power of distinct natural numbers.

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Question 7Multiple choiceMEDIUM

Question 7

Select the correct alternative from the given choices.

Answer the questions on the basis of the information given below.

Three non-zero single digits are in A.P. If the sum of all three-digit numbers formed by using these three digits exactly once is divisible by 15, then the minimum possible product of digits is:

Choose an answer

A.15B.35C.45D.80

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Question 8Multiple choiceEASY

Question 8

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A three-digit number has each of its digit less than 5. The sum of the number and its reverse is:

Choose an answer

A.a prime numberB.a palindromeC.an odd numberD.a multiple of 101

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Question 9Multiple choiceHARD

Question 9

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A shopkeeper has 150 gms, 70 gms, 20 gms, 15 gms, 5 gms and 2 gms pockets of chaat masala. He has to give 89 gms, 233 gms and 377 gms of chaat masala to three different persons. How many minimum number of pockets the shopkeeper will have to give to these three different persons?

Choose an answer

A.21B.19C.16D.12

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Question 10Multiple choiceEASY

Question 10

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Sum of five consecutive even natural numbers is 20 times a perfect square. Which of the following can be one of them?

Choose an answer

A.4B.8C.10 D.32

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Question 11Multiple choiceMEDIUM

Question 11

The maximum possible common difference between the digits is:

Answer the questions on the basis of the information given below.

Three non-zero single digits are in A.P. If the sum of all three-digit numbers formed by using these three digits exactly once is divisible by 15, then the minimum possible product of digits is:

Choose an answer

A.1B.2C.3D.4

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Question 12Multiple choiceMEDIUM

Question 12

Select the correct alternative from the given choices.

Choose the correct alternative.

The integers 1, 2, …, 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the number left on the board at the end?

Choose an answer

A.820B.821C.781D.819E.780

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Question 13Multiple choiceEASY

Question 13

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Choose an answer

A.

B.

C.

D.

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Question 14Multiple choiceMEDIUM

Question 14

Select the correct alternative from the given choices.

The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?

Choose an answer

A.330B.300C.250D.400

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Question 15Type in the answerEASY

Question 15

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Ajay attempted to add ten two-digit numbers. One of -them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by?

 

Your answer

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Question 16Multiple choiceMEDIUM

Question 16

Select the correct alternative from the given choices.

A two digit number ab is 60% of x. The two-digit number formed by reversing the digits of ab is 60% more than x. Find x.

 

Choose an answer

A.45B.54C.63D.72

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Common mistakes

• Allowing a leading zero in a number with a specified digit length.
• Assuming a pattern found in a few examples is a proof.

Practical solving approaches

• Represent digits explicitly with their allowed ranges.
• Use parity, divisibility and upper or lower bounds to reduce cases before enumeration.

Number properties & digits FAQs

How can I express a two-digit number algebraically?

If its tens digit is a and units digit is b, write it as 10a + b, with a from one to nine and b from zero to nine.

More Number Systems practice

• Base systems →
• Factorials & highest power →
• Factors, divisibility, HCF & LCM →
• Remainders & modular arithmetic →