Question : If 847 × 385 × 675 × 3025 = 3^a× 5^b× 7^c× 11^d, then the value of ab – cd is:
Option 1: 4
Option 2: 5
Option 3: 1
Option 4: 7

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Question : If a + b + c = 1, ab + bc + ca = –22 and abc = –40, then what is the value of a³+ b³ + c³?

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Answer 1

Correct Answer: 5

Solution : $847 \times 385 \times 675 \times 3025 = 3^{a} \times 5^{b} \times 7^{c} \times 11^{d}$
We can write the above numbers as
$847 = 11 \times 11 \times 7 = 11^{2} \times 7^{1}$
$385 = 5^{1} \times 7^{1} \times 11^{1}$
$675 = 3 \times 3 \times 3 \times 5 \times 5 = 3^{3} \times 5^{2}$
$3025 = 5 \times 5 \times 11 \times 11 = 5^{2} \times 11^{2}$
Now, we have
$847 \times 385 \times 675 \times 3025 = 3^{a} \times 5^{b} \times 7^{c} \times 11^{d}$
$\Rightarrow 11^{2} \times 7^{1} \times 5^{1} \times 7^{1} \times 11^{1} \times 3^{3} \times 5^{2} \times 5^{2} \times 11^{2} = 3^{a} \times 5^{b} \times 7^{c} \times 11^{d}$
$\Rightarrow 3^{3} \times 5^{5} \times 7^{2} \times 11^{5} = 3^{a} \times 5^{b} \times 7^{c} \times 11^{d}$
On comparing we get
$a = 3, b = 5, c = 2$ and $d = 5$
Now, $ab - cd = (3 \times 5 - 2 \times 5) = (15 - 10) = 5$
Hence, the correct answer is 5.

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Question : If 847 × 385 × 675 × 3025 = 3a × 5b × 7c × 11d, then the value of ab – cd is:Option 1: 4Option 2: 5Option 3: 1Option 4: 7

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Question : If 847 × 385 × 675 × 3025 = 3^a× 5^b× 7^c× 11^d, then the value of ab – cd is:
Option 1: 4
Option 2: 5
Option 3: 1
Option 4: 7