1.

1). Quantity 1 > Quantity 2 2). Quantity 1 ≥ Quantity 2 3). Quantity 2 > Quantity 14). Quantity 2 ≥ Quantity 1

Answer»

Quantity 1:

If we fix 1 at the unit digit place than any other digit (7, 9) can be arranged in = 2! = 2

Which means there 2 numbers which have 1 at the unit place

If we observed we will find that there are 2 numbers each with 7 and 9 at the unit place.

SUM of all the numbers at the unit’s place is,

⇒ 1 × 2 + 7 × 2 + 9 × 2

⇒ 2 × (1 + 7 + 9)

⇒ 2 × (17) = 34

Sum of all the tens place = 34 × 10 = 340

Sum of all the hundred place = 34 × 100 = 34000

∴ Sum of all POSSIBLE numbers = 34 + 340 + 34000 = 34374

Quantity 2:

If we fix 1 at the unit digit place than any other digit (8, 7) can be arranged in = 2! = 2

Which means there 2 numbers which have 1 at the unit place

If we observed we will find that there 2 numbers each with 7 and 8 at the unit place

Sum of all the numbers at the unit’s place,

⇒ 1 × 2 + 7 × 2 + 8 × 2

⇒ 2 × (1 + 7 + 8)

⇒ 2 × (16) = 32

Sum of all the tens place = 32 × 10 = 320

Sum of all the hundred place = 32000

∴ Sum of all possible number = 32 + 320 + 32000 = 32352

We can see that ∴ Quantity 1 > Quantity 2



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