Expressions using Letter-Numbers — Hard

Q1. Krithika has x notes of Rs 100, y notes of Rs 20 and z notes of Rs 5. Consider these statements about her total amount: I. The expression for total is 100x + 20y + 5z. II. The expression for total is 100 + 20 + 5 + x + y + z. III. If x = 8, y = 4, z = 3, the total is Rs 895.

• A. I only
• B. I and III only
• C. II and III only
• D. All three

Q2. In a calendar month, a 2 × 3 grid of dates is chosen. The bottom middle cell has date w. What is the date in the top-right cell (one row up, one column right)?

• A. w + 1
• B. w - 1
• C. w - 6
• D. w + 6

Q3. A snail climbs u cm up the wall of a well during the day and slips d cm at night. This continues for 10 days and 10 nights. The expression for how far the snail is from its starting position after this period is

• A. 10(u - d) cm
• B. 10u - d cm
• C. u - 10d cm
• D. 10ud cm

Q4. Pushpita sells flowers on Independence Day. p customers bought only champak, q bought only marigold, and r customers bought BOTH. She gave a small flag to every customer. How many flags did she give away?

• A. p + q + 2r
• B. 2(p + q + r)
• C. p + q + r + 2
• D. p + q + r

Q5. One plate of jowar roti costs Rs 30 and one plate of pulao costs Rs 20. In a day x plates of jowar roti and y plates of pulao are sold. Which expression gives the total amount in rupees earned that day?

• A. (30 + 20) × (x + y)
• B. 30x + 20y
• C. 30x - 20y
• D. (30 + 20) × x + y

Q6. Consider these three statements about the Mind the Mistake item 'If a = -4, then 10 - a = 6': I. The student treated 10 - a as 10 - 4 = 6, forgetting the negative sign. II. The correct value is 10 - (-4) = 14. III. The correct value is 6.

• A. I and II only
• B. I and III only
• C. II and III only
• D. All three

Q7. A Mind the Mistake card says: 'If s = 7, then 3s - 2 = 15'. What is the correct value, and where is the mistake?

• A. 15 — there is no mistake
• B. 16 — the student multiplied 3 × 7 incorrectly
• C. 19 — the student computed 3 × 7 - 2 correctly only after fixing the wrong subtraction (15 came from 3 × (7-2) + 2)
• D. 21 — the student forgot to subtract

Q8. Assertion (A): When j = 5, the expression 2j has the value 10. Reason (R): 2j is short for 2 × j, so we replace j by 5 and multiply.

• A. Both A and R are true, and R is the correct explanation of A.
• B. Both A and R are true, but R is NOT the correct explanation of A.
• C. A is true, R is false.
• D. A is false, R is true.

Q9. Using the distributive property, simplify 5(2w + 3x + 4w).

• A. 30w + 15x
• B. 10w + 15x + 20w
• C. 5w + 3x + 4w
• D. 9w + 3x

Q10. A shop rents chairs for Rs 40 and tables for Rs 75 each, refunding Rs 6 per chair and Rs 10 per table on return. If x chairs and y tables are rented, what is the net amount paid in simplest form?

• A. 46x + 85y
• B. 34x + 65y
• C. 40x + 75y - 16
• D. (40 - 6)(x + y)

Q11. Simplify 2d - d - d - d.

• A. 0
• B. 2d
• C. -d
• D. d

Q12. Assertion (A): Simplifying 5 - (2 - 6z) gives 3 + 6z. Reason (R): When a minus sign is outside a bracket, every sign inside the bracket is reversed when the bracket is opened.

• A. Both A and R are true, and R is the correct explanation of A.
• B. Both A and R are true, but R is NOT the correct explanation of A.
• C. A is true, R is false.
• D. A is false, R is true.

Q13. Figure it Out Mind the Mistake item 10 shows the expression 3(j + 2k + 3h + 4) wrongly simplified as 3j + 6k + 9h + 12. What is the correct conclusion?

• A. 3j + 6k + 9h + 12 is incorrect; the correct simplest form is 3j + 6k + 9h
• B. Both forms equal the original
• C. 3j + 6k + 9h + 12 is wrong because 3 × 4 = 7
• D. 3j + 6k + 9h + 12 is actually the correct simplest form

Q14. On a saree border, design A occurs at positions 3n - 2, design B at 3n - 1, and design C at 3n. Which design appears at position 122?

• A. Design A
• B. Design B
• C. Design C
• D. None of A, B, C

Q15. In a traffic-signal sequence, red appears at positions 4n - 3, yellow at 2n, and green at 4n - 1. What colour is at position 90?

• A. Red
• B. Green
• C. Yellow
• D. It cannot be decided