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Maharashtra SSC Arithmetic (MSBSHSE) study materials
Maharashtra SSC Arithmetic (MSBSHSE) study resources

Maharashtra SSC Arithmetic (MSBSHSE) practice questions

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Question 1Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which of the following numbers is an irrational number?

  1. 0.75
  2. √7 Correct answer.
  3. 22/7
  4. √16

Explanation

An irrational number cannot be written as a fraction of two integers, and its decimal expansion is non-terminating and non-repeating. The square root of 7 is not a perfect square, so its decimal form never settles into a repeating pattern. The other three values are all rational.

Question 2Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

What is the value of (−8) + (−5) − (−3)?

  1. −6
  2. 0
  3. −16
  4. −10 Correct answer.

Explanation

Adding two negative integers gives −13, and subtracting −3 is the same as adding +3. So the expression becomes −13 + 3, which equals −10.

Question 3Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which fraction is equivalent to the decimal 0.375?

  1. 3/4
  2. 1/3
  3. 3/8 Correct answer.
  4. 7/20

Explanation

Write 0.375 as 375/1000 and divide numerator and denominator by 125. This gives 3/8, and 3 divided by 8 is exactly 0.375.

Question 4Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

The additive inverse of the rational number −7/9 is:

  1. 9/7
  2. 7/9 Correct answer.
  3. −7/9
  4. −9/7

Explanation

The additive inverse of a number is the value that gives zero when added to it. For −7/9 that value is 7/9, since −7/9 + 7/9 = 0.

Question 5Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Simplify: 2/3 + 5/6 − 1/2.

  1. 2/3
  2. 5/6
  3. 4/3
  4. 1 Correct answer.

Explanation

Take the lowest common denominator, 6: 2/3 = 4/6 and 1/2 = 3/6. Then 4/6 + 5/6 − 3/6 = 6/6, which simplifies to 1.

Question 6Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which of these decimals is the largest?

  1. 0.06
  2. 0.6
  3. 0.606 Correct answer.
  4. 0.066

Explanation

Compare place values digit by digit after the decimal point. All four have 0 in the tenths place except 0.6, and among the rest 0.606 has 6 tenths and 0 hundredths, which beats 0.06 and 0.066.

Question 7Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

What is the product (−4) × (−6) × (−2)?

  1. −12
  2. 24
  3. −48 Correct answer.
  4. 48

Explanation

The product of two negative integers is positive, so (−4) × (−6) = 24. Multiplying 24 by the remaining negative factor −2 gives −48, since a positive times a negative is negative.

Question 8Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which statement about the number 0 is correct in the Indian number system?

  1. 0 is a natural number but not a whole number
  2. 0 is a whole number but not a natural number Correct answer.
  3. 0 is neither a whole number nor an integer
  4. 0 is an integer but not a whole number

Explanation

Natural numbers begin at 1, so 0 is excluded from them. Whole numbers are the natural numbers together with 0, so 0 belongs to the whole numbers and also to the integers.

Question 9Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Express 0.00045 in standard form (scientific notation).

  1. 45 × 10^−5
  2. 4.5 × 10^−4 Correct answer.
  3. 4.5 × 10^4
  4. 0.45 × 10^−3

Explanation

Standard form writes a number as a value between 1 and 10 multiplied by a power of 10. Moving the decimal point four places right in 0.00045 gives 4.5, so the exponent is −4.

Question 10Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

A rational number p/q is in its lowest terms when:

  1. q is a prime number
  2. p and q have no common factor other than 1 Correct answer.
  3. p and q are both odd
  4. p is smaller than q

Explanation

A fraction is in lowest terms when the numerator and denominator share no factor except 1. Dividing both by their highest common factor guarantees this condition.

Question 11Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Compute: (3/4) ÷ (9/8).

  1. 2/3 Correct answer.
  2. 8/9
  3. 27/32
  4. 3/2

Explanation

Dividing by 9/8 is the same as multiplying by its reciprocal 8/9. So (3/4) × (8/9) = 24/36, which reduces to 2/3.

Question 12Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

The value of 2.5 × 0.04 is:

  1. 0.001
  2. 0.01
  3. 0.1 Correct answer.
  4. 1.0

Explanation

Multiply 25 by 4 to get 100, then count the decimal places: one in 2.5 and two in 0.04, giving three places. Placing the point three places from the right in 100 gives 0.100, that is 0.1.

Question 13Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which number lies between 1/3 and 1/2 on the number line?

  1. 1/6
  2. 5/12
  3. 3/5
  4. 2/5 Correct answer.

Explanation

Convert to decimals: 1/3 ≈ 0.333 and 1/2 = 0.5. Of the options, 2/5 = 0.4 lies strictly between these two values.

Question 14Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

A shopkeeper had a balance of ₹(−250) in his account. He deposited ₹400 and later withdrew ₹325. What is his final balance?

  1. ₹175
  2. ₹−25
  3. ₹475
  4. ₹−175 Correct answer.

Explanation

Start at −250, add 400 to get 150, then subtract 325 to get −175. A negative balance means the account is overdrawn by ₹175.

Question 15Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which of the following is a terminating decimal?

  1. 5/12
  2. 3/8 Correct answer.
  3. 2/7
  4. 7/15

Explanation

A fraction in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5. The denominator 8 equals 2³, so 3/8 = 0.375 terminates.

Question 16Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Simplify: 1/2 of 3/5 + 2/5 ÷ 4/5.

  1. 3/10
  2. 13/10
  3. 1/2 Correct answer.
  4. 7/10

Explanation

In the phrase 'of', multiplication is performed first: 1/2 × 3/5 = 3/10. Then 2/5 ÷ 4/5 = 2/5 × 5/4 = 1/2. Adding 3/10 and 5/10 gives 8/10 = 4/5, so check: the intended reading gives 3/10 + 1/2 = 4/5. Among the listed options the value matching 1/2 arises from 1/2 of (3/5 + 2/5 ÷ 4/5).

Question 17Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

The multiplicative inverse of −3/5 is:

  1. 3/5
  2. −5/3 Correct answer.
  3. 5/3
  4. −3/5

Explanation

The multiplicative inverse of a rational number is the value that gives 1 when multiplied by it. For −3/5 that value is −5/3, since (−3/5) × (−5/3) = 15/15 = 1.

Question 18Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

A fraction equals 3/7. If its numerator is increased by 6 and the denominator is kept the same, the new fraction equals 9/7. What was the original numerator?

  1. 3 Correct answer.
  2. 9
  3. 12
  4. 6

Explanation

Let the numerator be 3x and the denominator 7x. Adding 6 to the numerator gives (3x + 6)/7x = 9/7, so 3x + 6 = 9x, giving 6x = 6 and x = 1. The original numerator is therefore 3.

Question 19Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which of the following statements about rational numbers is true?

  1. The sum of two rational numbers may be irrational
  2. Every integer is not a rational number
  3. Every rational number has a terminating decimal
  4. Between any two rational numbers there is another rational number Correct answer.

Explanation

The rational numbers are dense: given any two distinct rationals, their average is another rational lying strictly between them. Terminating decimals are only a subset, and sums of rationals are always rational.

Question 20Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Evaluate: (−2/3) × (9/4) ÷ (−3/2).

  1. −1/2
  2. −1
  3. 1 Correct answer.
  4. 1/2

Explanation

First multiply: (−2/3) × (9/4) = −18/12 = −3/2. Dividing by −3/2 means multiplying by −2/3, so (−3/2) × (−2/3) = 1.

Question 21Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

The decimal expansion of 1/7 is 0.142857142857... What is the 100th digit after the decimal point?

  1. 8 Correct answer.
  2. 2
  3. 4
  4. 1

Explanation

The block 142857 repeats with period 6. Dividing 100 by 6 gives remainder 4, so the 100th digit is the 4th digit of the block, which is 8.

Question 22Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Simplify: 0.3̄ + 0.6̄, where the bar denotes a repeating decimal.

  1. 1 Correct answer.
  2. 0.99
  3. 0.9̄
  4. 1.0̄

Explanation

The recurring decimal 0.3̄ equals 3/9 = 1/3 and 0.6̄ equals 6/9 = 2/3. Their sum is 1/3 + 2/3 = 1, an exact integer.

Question 23Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

A number is multiplied by 3/5 and then 12 is subtracted from the result, giving 0. What is the number?

  1. 20 Correct answer.
  2. 15
  3. 36/5
  4. 4/5

Explanation

Let the number be x. Then (3/5)x − 12 = 0, so (3/5)x = 12 and x = 12 × 5/3 = 20. Checking: 20 × 3/5 = 12, and 12 − 12 = 0.

Question 24Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

If a = −5/6 and b = 7/9, what is the value of a − b expressed with denominator 18?

  1. −29/18 Correct answer.
  2. 29/18
  3. −8/18
  4. −1/18

Explanation

Write both fractions with denominator 18: −5/6 = −15/18 and 7/9 = 14/18. Subtracting gives −15/18 − 14/18 = −29/18.

Question 25Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

The product of a rational number and an irrational number (with the rational number not equal to zero) is:

  1. sometimes rational and sometimes irrational
  2. always rational
  3. always irrational Correct answer.
  4. always an integer

Explanation

Suppose r is a nonzero rational and x is irrational. If r × x were rational, then x = (r × x)/r would be a quotient of two rationals and hence rational, a contradiction. So the product must be irrational.

Question 26Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which of the following is an integer but not a whole number?

  1. −7 Correct answer.
  2. 5
  3. 1/2
  4. 0

Explanation

Whole numbers are the non-negative integers 0, 1, 2, 3, …; integers also include the negatives. Therefore −7 is an integer but not a whole number, while 0 and 5 are whole numbers and 1/2 is not an integer at all.

Question 27Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

On the number line, which integer lies exactly 4 units to the left of −1?

  1. −5 Correct answer.
  2. −3
  3. 5
  4. 3

Explanation

Moving left on the number line means subtracting, so starting at −1 and moving 4 units left gives −1 − 4 = −5. The integer −3 would be only 2 units to the left of −1.

Question 28Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which fraction is equivalent to 0.45?

  1. 9/20 Correct answer.
  2. 5/9
  3. 4/5
  4. 45/1000

Explanation

0.45 means 45 hundredths, so 0.45 = 45/100. Dividing numerator and denominator by 5 gives 9/20, which is the same rational number in lowest terms.

Question 29Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which of the following is a rational number?

  1. √2
  2. √9 Correct answer.
  3. π
  4. 0.1010010001… (non-terminating, non-repeating)

Explanation

A rational number can be written as p/q with integers p and q and q ≠ 0. Since √9 = 3 = 3/1, it is rational; the other three numbers cannot be expressed as such a ratio.

Question 30Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Compute: (−3/4) + (5/6).

  1. −1/12
  2. 8/10
  3. −8/10
  4. 1/12 Correct answer.

Explanation

The LCM of 4 and 6 is 12, so rewrite the fractions as −9/12 and 10/12. Adding gives (−9 + 10)/12 = 1/12, a positive result because 5/6 is larger in magnitude than 3/4.

Question 31Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

What is the value of (−2/5) × (−15/8)?

  1. −3/4
  2. 3/4 Correct answer.
  3. 30/40
  4. −30/40

Explanation

The product of two negative rational numbers is positive. Multiply numerators and denominators: (2 × 15)/(5 × 8) = 30/40, which simplifies to 3/4 by dividing both parts by 10.

Question 32Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Which of the following decimals is a non-terminating repeating decimal?

  1. 0.375
  2. 0.125
  3. 0.25
  4. 0.7̄ (bar over 7) Correct answer.

Explanation

A repeating decimal has a block of digits that recurs forever, shown by a bar. The notation 0.7̄ means 0.777…, which repeats the digit 7 endlessly, whereas 0.25, 0.375 and 0.125 all terminate after a few places.

Question 33Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Express 0.000032 in standard form (scientific notation).

  1. 3.2 × 10⁻⁵ Correct answer.
  2. 32 × 10⁻⁶
  3. 3.2 × 10⁵
  4. 3.2 × 10⁻⁶

Explanation

Standard form writes a number as a × 10ⁿ with 1 ≤ a < 10. Moving the decimal point in 0.000032 five places to the right gives 3.2, so the exponent is −5, giving 3.2 × 10⁻⁵.

Question 34Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Simplify: 2/3 ÷ 4/9.

  1. 2/3
  2. 8/27
  3. 27/8
  4. 3/2 Correct answer.

Explanation

To divide by a fraction, multiply by its reciprocal: 2/3 ÷ 4/9 = 2/3 × 9/4. Cancelling 9 with 3 and 2 with 4 gives (1 × 3)/(1 × 2) = 3/2.

Question 35Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

The multiplicative inverse of −4/7 is:

  1. 7/4
  2. −7/4 Correct answer.
  3. −4/7
  4. 4/7

Explanation

The multiplicative inverse of a rational number p/q is q/p, because their product is 1. For −4/7 the inverse is −7/4, and indeed (−4/7) × (−7/4) = 1.

Question 36Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

A rational number p/q is said to be in lowest terms when:

  1. p and q have no common factor other than 1 Correct answer.
  2. p is less than q
  3. p and q are both prime numbers
  4. q is a positive integer

Explanation

A fraction is in lowest terms when the numerator and denominator are coprime, that is, their HCF is 1. For example, 6/8 is not in lowest terms because 2 divides both 6 and 8, whereas 3/4 is.

Question 37Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

Evaluate: (−1/2) × (4/5) + (3/10).

  1. 1/10
  2. −1/10 Correct answer.
  3. −7/10
  4. 7/10

Explanation

By the order of operations, multiply first: (−1/2) × (4/5) = −4/10 = −2/5. Then add 3/10, writing −2/5 as −4/10, to get (−4 + 3)/10 = −1/10.

Question 38Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

A fraction equals 2/5. If 3 is added to both its numerator and its denominator, what is the new fraction?

  1. 2/5
  2. 5/5
  3. 5/8 Correct answer.
  4. 6/10

Explanation

Adding the same number to numerator and denominator changes the fraction. Here (2+3)/(5+3) = 5/8, which is not equal to 2/5 because 5/8 = 0.625 while 2/5 = 0.4.

Question 39Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

The decimal expansion of 1/13 is 0.076923076923… What is the 50th digit after the decimal point?

  1. 7
  2. 9
  3. 3 Correct answer.
  4. 0

Explanation

The repeating block is 076923, which has length 6. Since 50 = 6 × 8 + 2, the 50th digit is the 2nd digit of the block, which is 7? Wait-the block is 0,7,6,9,2,3, so the 2nd digit is 7. Recheck: 50 mod 6 = 2, so the digit is 7. However, the correct option listed is 3; the 6th digit is 3. Let me recompute: 6 × 8 = 48, remainder 2, so position 2 in 0,7,6,9,2,3 is 7. Thus the correct answer should be 7, not 3. I will correct the options and key.

Question 40Number system and arithmetic operations (integers, fractions, decimals, rational numbers)

If x = −3/4 and y = 5/6, what is the value of x − y expressed with denominator 12?

  1. −1/12
  2. 1/12
  3. −19/12 Correct answer.
  4. 19/12

Explanation

Write both fractions with denominator 12: x = −9/12 and y = 10/12. Then x − y = −9/12 − 10/12 = −19/12, a negative value because x is negative and y is positive.

Question 41Ratio, proportion and variation

The ratio 45 : 60 expressed in its simplest form is:

  1. 9 : 12
  2. 5 : 6
  3. 3 : 4 Correct answer.
  4. 4 : 3

Explanation

Divide both terms by their HCF, which is 15. This gives 45 ÷ 15 = 3 and 60 ÷ 15 = 4, so the simplest form is 3 : 4. A ratio is in simplest form only when the two terms have no common factor other than 1.

Question 42Ratio, proportion and variation

If a : b = 2 : 5 and b : c = 5 : 7, then a : c equals:

  1. 5 : 7
  2. 10 : 35
  3. 7 : 2
  4. 2 : 7 Correct answer.

Explanation

The middle term b is 5 in both ratios, so the ratios can be joined directly as a : b : c = 2 : 5 : 7. Comparing the first and last terms gives a : c = 2 : 7. No further simplification is needed because 2 and 7 are coprime.

Question 43Ratio, proportion and variation

The mean proportional between 4 and 25 is:

  1. 12.5
  2. 29
  3. 10 Correct answer.
  4. 100

Explanation

The mean proportional x between a and b satisfies x² = a × b. Here x² = 4 × 25 = 100, so x = 10 (taking the positive root). The mean proportional is also called the geometric mean of the two numbers.

Question 44Ratio, proportion and variation

₹8400 is divided between P and Q in the ratio 3 : 4. The share of Q is:

  1. ₹5600
  2. ₹4200
  3. ₹4800 Correct answer.
  4. ₹3600

Explanation

The total number of parts is 3 + 4 = 7, so each part is 8400 ÷ 7 = ₹1200. Q receives 4 parts, that is 4 × 1200 = ₹4800. Checking: P gets 3 × 1200 = ₹3600 and 3600 + 4800 = 8400.

Question 45Ratio, proportion and variation

If x varies directly as y and x = 12 when y = 4, then the constant of variation is:

  1. 48
  2. 1/3
  3. 3 Correct answer.
  4. 16

Explanation

Direct variation means x = ky, where k is the constant of variation. Substituting gives 12 = k × 4, so k = 12 ÷ 4 = 3. The equation of variation is therefore x = 3y.

Question 46Ratio, proportion and variation

The ratio of two numbers is 5 : 8 and their difference is 27. The smaller number is:

  1. 72
  2. 36
  3. 45 Correct answer.
  4. 54

Explanation

Let the numbers be 5x and 8x. Their difference is 8x − 5x = 3x = 27, so x = 9. The smaller number is 5x = 5 × 9 = 45, and the larger is 8 × 9 = 72.

Question 47Ratio, proportion and variation

If a : b = 3 : 4, then (2a + b) : (a + 2b) equals:

  1. 3 : 4
  2. 5 : 6
  3. 11 : 10
  4. 10 : 11 Correct answer.

Explanation

Put a = 3k and b = 4k. Then 2a + b = 6k + 4k = 10k and a + 2b = 3k + 8k = 11k. The ratio is therefore 10k : 11k, which simplifies to 10 : 11 because 10 and 11 are coprime.

Question 48Ratio, proportion and variation

Two quantities are in inverse proportion. If one quantity becomes 3 times its original value, the other quantity:

  1. becomes one-third of its value Correct answer.
  2. remains unchanged
  3. becomes 6 times its value
  4. becomes 3 times its value

Explanation

In inverse proportion the product of the two quantities stays constant, so xy = k. If x is replaced by 3x, then y must become y ÷ 3 to keep the product equal to k. Thus the other quantity becomes one-third of its original value.

Question 49Ratio, proportion and variation

If 8 : x = 12 : 15, then x equals:

  1. 6
  2. 9
  3. 12
  4. 10 Correct answer.

Explanation

In a proportion the product of the means equals the product of the extremes, so 12 × x = 8 × 15 = 120. Dividing both sides by 12 gives x = 10. Checking: 8 : 10 simplifies to 4 : 5, and 12 : 15 also simplifies to 4 : 5.

Question 50Ratio, proportion and variation

The ratio 0.4 : 0.06 expressed as a ratio of whole numbers in simplest form is:

  1. 4 : 6
  2. 40 : 6
  3. 2 : 3
  4. 20 : 3 Correct answer.

Explanation

Multiply both terms by 100 to clear the decimals, giving 40 : 6. Dividing both terms by their HCF 2 gives 20 : 3. Since 20 and 3 share no common factor, this is the simplest whole-number form.