60m + 65 = 61 (m + 1)

∴ 60m + 65 = 61m + 61

∴ m = 4

\(\sqrt{42}\) is more than 6 and \(\sqrt{58}\) is more than 7.

Hence the total is more than 10.

(In GRE square root of a number is always considered as positive)

Area of Δ = ¹⁄₂ base X height.

Base of ΔMNO is MO = MP + PO

Base of ΔPQR is PR = PO + QR

Since PO is same and MP is less than OR, the base MO is less than the base PR.

∴ To get the same area, altitude of ΔMNO will be greater than altitude of ΔPQR.

Pythagoras triplet 6, 8, 10

∴ Col. A =10, Col. B = 12

nth term of an A.P. = a + (n - 1)d

∴ Sum of middle 3 terms = sum of 5th, 6th and 7th term

= (a + 4d) + (a + 5d) + (a + 6d) = 3a + 15d

Sum of last three terms = sum of 9^th, 10^th and 11^th term = (a + 8d) + (a + 9d) + (a + 10d)

= 3a + 27d

∴ d=4,a=4

Col. A = a + 8d = 36, Col. B = 60

For independent events

P(A ∪ B) = P(A)+ P(B) - P(A).P(B)

= 0.6 + 0.8 - (0.6 × 0.8) = 0.92

∴ Col. A = Col. B

Let Cost Price of 20 apples and 15 figs = $100.

∴ Cost price of 4 apples and 3 figs =\(\frac{100}{5}\)= 20

Also Selling Price of 4 apples and 3 figs = \(\frac{100}{2}\) = $50

∴ Profit = $50 - $20 = $30

∴ Profit % = 30 × 100 = 150%

∴ Col. A = 150%, Col. B = 125%

Dick sold the car to Harry at a loss of 20%.

Let Tom sell the car to Dick for $100.

∴ Dick now sells it to Harry for 0.80 × 100= $80.

∴ Dick's cost price for the car = Tom's cost price for the car = $80.

∴ Car cost $80 to Tom and he sold it at $100.

∴ % gain = \(\frac{20}{80}\) × 100 = 25%

∴ Col. A > Col. B

Average speed = \(\frac{Total\, distance}{Total\, time}\)

Let distance travelled at each speed is 8 kms.

∴ Time taken = ⁸⁄₈,⁸⁄₄,⁸⁄₂ and ⁸⁄₁ hours respectively. Total time taken 15 hours.

∴ Total distance travelled = 32 kms.

∴ Average speed = \(\frac{32}{5}\) = 2 kmph. approx.

Col. A = 81¹⁶ = (3⁴)¹⁶ = 3⁶⁴

Col. B = (3³²)² = 3⁶⁴