Number System — Practice Questions – KLEE Arithmetic & Mental Ability Test 2
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Solved examples
What is the place value of 5 in 3254710?
Answer: 50000 — 5 is in the ten-thousands place: 5 × 10,000 = 50,000.
The face value of 8 in the number 458926 is:
Answer: 8 — The face value of a digit is the digit itself, whatever its position.
The sum of the place values of 3 in the number 503535 is:
Answer: 3030 — Place values of 3 are 3,000 and 30; 3,000 + 30 = 3,030.
The sum of the greatest and smallest numbers of five digits is:
Answer: 109,999 — 99,999 + 10,000 = 1,09,999.
If the largest three-digit number is subtracted from the smallest five-digit number, the remainder is:
Answer: 9001 — 10,000 − 999 = 9,001.
The smallest number of 5 digits beginning with 3 and ending with 5 is:
Answer: 30005 — Keep the middle digits as small as possible (zeros): 30,005.
What is the minimum four-digit number formed by using the digits 2, 4, 0, 7 once each?
Answer: 2047 — Arrange in ascending order but do not place 0 first: 2, 0, 4, 7 → 2,047.
All natural numbers and 0 are called the ______ numbers.
Answer: whole — Natural numbers together with 0 form the whole numbers.
Statements about natural numbers: (1) There is a smallest natural number. (2) There is a largest natural number. (3) Between two natural numbers there is always a natural number. Which is/are correct?
Answer: Only 1 — 1 is the smallest natural number; there is no largest; and nothing lies between consecutive natural numbers.
Every rational number is also:
Answer: a real number — Rational numbers are part of the real numbers.
The number π is:
Answer: an irrational number — π is a non-terminating, non-repeating decimal.
√2 is a/an:
Answer: irrational number — √2 is non-terminating and non-repeating.
The number √3 is:
Answer: an infinite non-recurring decimal — √3 is irrational; it is only approximately 1.732.
What is the sum of the squares of the digits from 1 to 9?
Answer: 285 — 9 × 10 × 19/6 = 285.
Practice questions
What is the place value of 6 in 4,36,182?
- A. 6,000
- B. 600
- C. 60,000
- D. 6
Answer: Option A
Explanation:
6 is in the thousands place: 6 × 1,000 = 6,000.
What is the place value of 9 in 7,09,354?
- A. 9
- B. 9,000
- C. 90,000
- D. 900
Answer: Option B
Explanation:
9 is in the thousands place: 9 × 1,000 = 9,000.
What is the place value of 3 in 83,12,457?
- A. 3,00,000
- B. 3,000
- C. 30,00,000
- D. 30,000
Answer: Option A
Explanation:
3 is in the lakhs place: 3 × 1,00,000 = 3,00,000.
What is the place value of 2 in 56,21,084?
- A. 20,000
- B. 2,000
- C. 2,00,000
- D. 200
Answer: Option A
Explanation:
2 is in the ten-thousands place: 2 × 10,000 = 20,000.
What is the place value of 7 in 9,07,615?
- A. 700
- B. 7
- C. 7,000
- D. 70,000
Answer: Option C
Explanation:
7 is in the thousands place: 7 × 1,000 = 7,000.
The face value of 3 in 73,452 is:
- A. 30
- B. 3
- C. 300
- D. 3,000
Answer: Option B
Explanation:
The face value of a digit never depends on its position, so it is 3.
What is the product of the place value and the face value of 6 in 2,62,145?
- A. 60,000
- B. 3,60,000
- C. 3,60,006
- D. 36,000
Answer: Option B
Explanation:
Place value = 60,000 and face value = 6; 60,000 × 6 = 3,60,000.
What is the difference between the place value and the face value of 4 in 1,43,762?
- A. 40,000
- B. 39,996
- C. 3,996
- D. 39,994
Answer: Option B
Explanation:
Place value = 40,000 and face value = 4; 40,000 − 4 = 39,996.
What is the sum of the face values of all the digits in 3,052?
- A. 3,052
- B. 9
- C. 11
- D. 10
Answer: Option D
Explanation:
3 + 0 + 5 + 2 = 10.
The face value of 9 in 9,00,001 is:
- A. 9,00,000
- B. 90,000
- C. 0
- D. 9
Answer: Option D
Explanation:
The face value is simply the digit, 9.
The sum of the place values of 4 in 4,24,143 is:
- A. 12
- B. 4,04,004
- C. 4,40,040
- D. 4,04,040
Answer: Option D
Explanation:
The 4s stand for 4,00,000, 4,000 and 40; their sum is 4,04,040.
The sum of the place values of 2 in 52,312 is:
- A. 4
- B. 2,020
- C. 2,200
- D. 2,002
Answer: Option D
Explanation:
The 2s stand for 2,000 and 2; their sum is 2,002.
The sum of the place values of 7 in 7,707 is:
- A. 7,707
- B. 7,077
- C. 7,770
- D. 21
Answer: Option A
Explanation:
The 7s stand for 7,000, 700 and 7; their sum is 7,707.
The sum of the place values of 5 in 15,450 is:
- A. 5,005
- B. 10
- C. 5,050
- D. 5,500
Answer: Option C
Explanation:
The 5s stand for 5,000 and 50; their sum is 5,050.
The sum of the place values of 1 in 1,10,101 is:
- A. 4
- B. 1,11,101
- C. 1,01,101
- D. 1,10,101
Answer: Option D
Explanation:
The 1s stand for 1,00,000, 10,000, 100 and 1; their sum is 1,10,101.
The sum of the greatest and smallest four-digit numbers is:
- A. 10,999
- B. 11,111
- C. 9,999
- D. 10,000
Answer: Option A
Explanation:
9,999 + 1,000 = 10,999.
The sum of the greatest and smallest three-digit numbers is:
- A. 1,000
- B. 1,099
- C. 1,199
- D. 999
Answer: Option B
Explanation:
999 + 100 = 1,099.
The sum of the greatest and smallest six-digit numbers is:
- A. 10,99,990
- B. 10,00,000
- C. 10,99,999
- D. 11,00,000
Answer: Option C
Explanation:
9,99,999 + 1,00,000 = 10,99,999.
The sum of the greatest and smallest four-digit numbers having all digits different is:
- A. 10,899
- B. 11,009
- C. 10,889
- D. 10,999
Answer: Option A
Explanation:
Greatest = 9,876 and smallest = 1,023; 9,876 + 1,023 = 10,899.
The sum of the greatest two-digit number and the smallest three-digit number is:
- A. 189
- B. 200
- C. 199
- D. 109
Answer: Option C
Explanation:
99 + 100 = 199.
If the largest four-digit number is subtracted from the smallest six-digit number, the result is:
- A. 90,001
- B. 9,001
- C. 99,001
- D. 90,000
Answer: Option A
Explanation:
1,00,000 − 9,999 = 90,001.
If the largest two-digit number is subtracted from the smallest four-digit number, the result is:
- A. 991
- B. 900
- C. 910
- D. 901
Answer: Option D
Explanation:
1,000 − 99 = 901.
If the smallest four-digit number is subtracted from the largest five-digit number, the result is:
- A. 89,999
- B. 98,000
- C. 98,999
- D. 99,000
Answer: Option C
Explanation:
99,999 − 1,000 = 98,999.
If the largest four-digit number is subtracted from the smallest five-digit number, the result is:
- A. 10
- B. 1
- C. 0
- D. 9,001
Answer: Option B
Explanation:
10,000 − 9,999 = 1.
If the largest five-digit number is subtracted from the smallest seven-digit number, the result is:
- A. 9,00,000
- B. 9,99,001
- C. 90,001
- D. 9,00,001
Answer: Option D
Explanation:
10,00,000 − 99,999 = 9,00,001.
The smallest six-digit number beginning with 7 and ending with 2 is:
- A. 7,00,002
- B. 7,00,012
- C. 7,10,002
- D. 7,00,000
Answer: Option A
Explanation:
Fill the middle four places with zeros: 7,00,002.
The largest five-digit number beginning with 4 and ending with 1 is:
- A. 49,981
- B. 49,991
- C. 49,999
- D. 41,991
Answer: Option B
Explanation:
Fill the middle three places with 9s: 49,991.
The smallest four-digit number beginning with 9 and ending with 9 is:
- A. 9,099
- B. 9,000
- C. 9,009
- D. 9,109
Answer: Option C
Explanation:
Fill the middle two places with zeros: 9,009.
The largest four-digit number beginning with 1 and ending with 8 is:
- A. 1,988
- B. 1,998
- C. 1,999
- D. 1,898
Answer: Option B
Explanation:
Fill the middle two places with 9s: 1,998.
The smallest five-digit even number beginning with 6 is:
- A. 60,002
- B. 60,000
- C. 61,000
- D. 60,001
Answer: Option B
Explanation:
60,000 begins with 6 and is even (it ends in 0).
What is the smallest four-digit number formed using the digits 5, 0, 3, 8 once each?
- A. 3,058
- B. 3,508
- C. 3,085
- D. 0,358
Answer: Option A
Explanation:
The smallest non-zero digit goes first (3), then the rest in ascending order: 3,058.
What is the largest four-digit number formed using the digits 5, 0, 3, 8 once each?
- A. 8,530
- B. 8,503
- C. 5,830
- D. 8,350
Answer: Option A
Explanation:
Arrange the digits in descending order: 8,530.
Find the difference between the largest and smallest four-digit numbers formed using 1, 0, 6, 9 once each.
- A. 8,631
- B. 8,451
- C. 9,610
- D. 8,541
Answer: Option D
Explanation:
Largest = 9,610 and smallest = 1,069; 9,610 − 1,069 = 8,541.
What is the smallest five-digit number formed using the digits 4, 0, 2, 9, 1 once each?
- A. 12,049
- B. 1,249
- C. 10,249
- D. 10,294
Answer: Option C
Explanation:
Smallest non-zero digit first (1), then 0, 2, 4, 9: 10,249.
What is the smallest four-digit EVEN number formed using the digits 3, 0, 7, 5 once each?
- A. 5,370
- B. 3,057
- C. 3,750
- D. 3,570
Answer: Option D
Explanation:
Only 0 is even, so it must be the last digit; arrange 3, 5, 7 in ascending order in front: 3,570.
All whole numbers together with the negatives of natural numbers are called:
- A. rational numbers only
- B. irrational numbers
- C. integers
- D. natural numbers
Answer: Option C
Explanation:
…, −2, −1, 0, 1, 2, … are the integers.
Numbers that can be written in the form p/q, where p and q are integers and q ≠ 0, are called:
- A. rational numbers
- B. natural numbers
- C. prime numbers
- D. irrational numbers
Answer: Option A
Explanation:
A ratio of two integers (q ≠ 0) is a rational number.
The smallest whole number is:
- A. 1
- B. There is no smallest whole number
- C. 0
- D. −1
Answer: Option C
Explanation:
Whole numbers begin at 0.
The smallest natural number is:
- A. 2
- B. −1
- C. 0
- D. 1
Answer: Option D
Explanation:
Natural (counting) numbers begin at 1.
A natural number greater than 1 having exactly two distinct factors (1 and itself) is called a:
- A. composite number
- B. prime number
- C. perfect number
- D. co-prime number
Answer: Option B
Explanation:
That is the definition of a prime number.
Statements about whole numbers: (1) There is a smallest whole number. (2) There is a largest whole number. (3) Every natural number is a whole number. Which is/are correct?
- A. Only 1
- B. 1 and 3
- C. Only 3
- D. 1, 2 and 3
Answer: Option B
Explanation:
0 is the smallest whole number and every natural number is whole; but there is no largest whole number.
Statements about integers: (1) There is a smallest integer. (2) There is no largest integer. (3) There is no integer between two consecutive integers. Which is/are correct?
- A. 1, 2 and 3
- B. 2 and 3
- C. 1 and 3
- D. Only 2
Answer: Option B
Explanation:
Integers go on forever in both directions, so (1) is false; (2) and (3) are true.
Statements about rational numbers: (1) Between any two rational numbers there is another rational number. (2) Every integer is a rational number. (3) Every rational number is an integer. Which is/are correct?
- A. 2 and 3
- B. 1, 2 and 3
- C. Only 1
- D. 1 and 2
Answer: Option D
Explanation:
(a+b)/2 always lies between a and b, and n = n/1; but 1/2 is rational and not an integer.
Statements about prime numbers: (1) 2 is the only even prime. (2) 1 is a prime number. (3) There are infinitely many primes. Which is/are correct?
- A. 1 and 3
- B. 1 and 2
- C. 1, 2 and 3
- D. Only 1
Answer: Option A
Explanation:
1 has only one factor, so it is not prime; the other two statements are true.
Statements about zero (with natural numbers starting at 1): (1) 0 is a natural number. (2) 0 is a whole number. (3) 0 is an integer. Which is/are correct?
- A. Only 2
- B. 1 and 2
- C. 2 and 3
- D. 1, 2 and 3
Answer: Option C
Explanation:
Natural numbers start at 1, so (1) is false; 0 is both a whole number and an integer.
Every integer is also:
- A. a natural number
- B. a rational number
- C. an irrational number
- D. a whole number
Answer: Option B
Explanation:
Any integer n can be written as n/1, so it is rational.
Every whole number is also:
- A. a positive number
- B. a natural number
- C. a prime number
- D. an integer
Answer: Option D
Explanation:
Whole numbers 0, 1, 2, … all belong to the integers. (0 is whole but not natural or positive.)
Every natural number is also:
- A. an irrational number
- B. a prime number
- C. a whole number
- D. an even number
Answer: Option C
Explanation:
Natural numbers 1, 2, 3, … are all whole numbers.
Every irrational number is also:
- A. a whole number
- B. an integer
- C. a rational number
- D. a real number
Answer: Option D
Explanation:
Irrational numbers such as √2 and π are real numbers.
Which of the following is NOT always a rational number?
- A. An integer
- B. A recurring decimal
- C. A terminating decimal
- D. The square root of a positive integer
Answer: Option D
Explanation:
√4 = 2 is rational but √2 is not, so square roots of integers are not always rational.
The number √5 is:
- A. a recurring decimal
- B. an irrational number
- C. an integer
- D. a rational number
Answer: Option B
Explanation:
5 is not a perfect square, so √5 is non-terminating and non-repeating.
The number 22/7 is:
- A. a rational number
- B. an integer
- C. an irrational number
- D. a natural number
Answer: Option A
Explanation:
22/7 is a ratio of two integers, so it is rational (it is only an approximation of π).
The recurring decimal 0.333… is:
- A. an irrational number
- B. a rational number
- C. an integer
- D. not a real number
Answer: Option B
Explanation:
0.333… = 1/3, so it is rational.
The number √16 is:
- A. not a real number
- B. an irrational number
- C. a negative number
- D. a natural number
Answer: Option D
Explanation:
√16 = 4, a natural number.
Which of the following is an irrational number?
- A. 0.25
- B. √9
- C. √7
- D. 3/4
Answer: Option C
Explanation:
7 is not a perfect square, so √7 is irrational; √9 = 3, 0.25 = 1/4.
Which of the following is a rational number?
- A. √49
- B. √3
- C. π
- D. √5
Answer: Option A
Explanation:
√49 = 7, a rational number.
Which of the following is irrational?
- A. 1.25
- B. √12
- C. √0.04
- D. √25
Answer: Option B
Explanation:
√25 = 5, √0.04 = 0.2 and 1.25 = 5/4 are rational; √12 = 2√3 is irrational.
The number √2 + 3 is:
- A. a natural number
- B. irrational
- C. rational
- D. an integer
Answer: Option B
Explanation:
A rational number plus an irrational number is irrational.
The number √2 × √2 is:
- A. rational
- B. imaginary
- C. undefined
- D. irrational
Answer: Option A
Explanation:
√2 × √2 = 2, which is rational.
Which of the following is irrational?
- A. 0.101010… (repeating)
- B. 0.25
- C. 1/7
- D. 0.1010010001… (the number of 0s keeps increasing)
Answer: Option D
Explanation:
A non-terminating decimal with no repeating block is irrational.
The number √5 is:
- A. an infinite recurring decimal
- B. exactly 2.236
- C. an infinite non-recurring decimal
- D. a finite decimal
Answer: Option C
Explanation:
√5 is irrational, so its decimal never ends and never repeats.
1/3 written as a decimal is:
- A. a finite decimal
- B. an infinite recurring decimal
- C. an infinite non-recurring decimal
- D. an integer
Answer: Option B
Explanation:
1/3 = 0.333…, which repeats forever.
3/8 written as a decimal is:
- A. an integer
- B. a recurring decimal
- C. a non-terminating non-recurring decimal
- D. a terminating decimal
Answer: Option D
Explanation:
3/8 = 0.375 — the denominator has only 2 as a prime factor, so it terminates.
The decimal expansion of π is:
- A. exactly 3.14
- B. terminating
- C. non-terminating and recurring
- D. non-terminating and non-recurring
Answer: Option D
Explanation:
π is irrational.
2/11 written as a decimal is:
- A. an infinite recurring decimal
- B. an integer
- C. a finite decimal
- D. an infinite non-recurring decimal
Answer: Option A
Explanation:
2/11 = 0.1818…, repeating '18'.
What is 1² + 2² + … + 8²?
- A. 204
- B. 196
- C. 140
- D. 285
Answer: Option A
Explanation:
8 × 9 × 17/6 = 204.
What is 1² + 2² + … + 11²?
- A. 385
- B. 496
- C. 506
- D. 650
Answer: Option C
Explanation:
11 × 12 × 23/6 = 506.
What is the sum of the squares of the first 6 natural numbers?
- A. 140
- B. 91
- C. 81
- D. 55
Answer: Option B
Explanation:
6 × 7 × 13/6 = 91.
What is 2² + 4² + 6² + 8² + 10²?
- A. 200
- B. 110
- C. 385
- D. 220
Answer: Option D
Explanation:
= 4(1² + 2² + 3² + 4² + 5²) = 4 × 55 = 220.
What is 1² + 2² + … + 25²?
- A. 5,525
- B. 5,625
- C. 5,252
- D. 4,900
Answer: Option A
Explanation:
25 × 26 × 51/6 = 5,525.