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For all positive integers a and b, the expression a!b is defined as a
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10 Mar 2022, 04:00
10 Mar 2022, 04:00
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For all positive integers a and b, the expression a!b is defined as a * b plus the greatest prime factor of a * b. For example, 3!2 = 6 + 3 = 9. If 4!b = 55, then what is b?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Re: For all positive integers a and b, the expression a!b is defined as a
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10 Mar 2022, 20:43
10 Mar 2022, 20:43
1
\(a!b = a * b +\) the greatest prime factor of \(a * b.\)
\(4!b = 4b +\) greatest prime no of \(4b = 55\)
The only possible value for \(b\) can be \(11\) (we can try from options as well)
Answer B
\(4!b = 4b +\) greatest prime no of \(4b = 55\)
The only possible value for \(b\) can be \(11\) (we can try from options as well)
Answer B
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Re: For all positive integers a and b, the expression a!b is defined as a
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21 Aug 2022, 10:10
21 Aug 2022, 10:10
Given that a!b = a * b + the greatest prime factor of a * b and 4!b = 55 and we need to find the value of b
4!b = 4 * b + the greatest prime factor of 4 * b = 55 (Given)
Now, we can take each answer choice and check which one satisfies this. Before we do that let's use some logic to eliminate answer choices
The greatest prime factor of 4 * b has to be ≥ 2 as 2 is a prime factor of 4
=> 4*b + something positive = 55 => 4*b cannot be more than 55
E. So, 14 is ruled out as 4*14 = 56 => FALSE
D. Similarly, 4*13 = 52 and 13 itself is prime so 4*13 + 13 will be greater than 55 => FALSE
C. Let's try backwards and try 12
4*12 + the greatest prime factor of 4 * 12 = 48 + 3 = 51 => FALSE
B. 4*11 + the greatest prime factor of 4 * 11 = 44 + 11 = 55 => TRUE
In actual test you can mark and move on but I am solving for A to complete the solution.
A. 4*10 + the greatest prime factor of 4 * 10 = 40 + 5 = 45 => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
4!b = 4 * b + the greatest prime factor of 4 * b = 55 (Given)
Now, we can take each answer choice and check which one satisfies this. Before we do that let's use some logic to eliminate answer choices
The greatest prime factor of 4 * b has to be ≥ 2 as 2 is a prime factor of 4
=> 4*b + something positive = 55 => 4*b cannot be more than 55
E. So, 14 is ruled out as 4*14 = 56 => FALSE
D. Similarly, 4*13 = 52 and 13 itself is prime so 4*13 + 13 will be greater than 55 => FALSE
C. Let's try backwards and try 12
4*12 + the greatest prime factor of 4 * 12 = 48 + 3 = 51 => FALSE
B. 4*11 + the greatest prime factor of 4 * 11 = 44 + 11 = 55 => TRUE
In actual test you can mark and move on but I am solving for A to complete the solution.
A. 4*10 + the greatest prime factor of 4 * 10 = 40 + 5 = 45 => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
