HOT Competition 27 Aug/8AM: When the digits of two-digit positive inte

Question

When the digits of two-digit positive integer m are reversed, the result is two-digit positive integer n. What is the largest integer that must be a factor of 4m - 7n?

A. 1
B. 9
C. 11
D. 33
E. 99

Varunsawhney8 · Accepted Answer

When the digits of two-digit positive integer m are reversed, the result is two-digit positive integer n. What is the largest integer that must be a factor of 4m - 7n?

Let 2 digit positve number m= ab
Reverse of m = n = ba

We know m=10a+b and n=10b+a
in the exp.
4m-7a
=40a+4b-(70b+7a)
=33a-66b
taking 33 common
=33(a-2b)

So largest integer is 33
Answer: D

Posted from my mobile device

expandhorizons · Answer

One way to represent a 2-digit number is 10x+y in which x and y are the 2 digits.

For ex: 45 can be expanded as 10*4+5 and its reverse 54 can be represented as 10*5 + 4

So, let's assume m is equal to 10x+y then n would be equal to 10y+x

4m - 7n would become 4(10x+y) - 7(10y+x)

=> 40x + 4y - 70y - 7x

=> 33x - 66y

=> 33(x - 2y)
Therefore, the largest factor would be 33

Hence D is the answer

TarunKumar1234 · Answer

m= 10x+y and n= 10y+x

Given, 4m-7n = 40x+4y- 70y-7x= 33x - 66y = 33(x-2y). So largest factor can be 33.

So, I think, D.

binsnitin11 · Answer

When the digits of two-digit positive integer m are reversed, the result is two-digit positive integer n. What is the largest integer that must be a factor of 4m - 7n?

A. 1
B. 9
C. 11
D. 33
E. 99

let m = ab or 10a + b 
then n = ba or 10b + a

Aco. to equation: 4m-7n = 4(10a+b) - 7(10b+a)
40a+4b - 70b-7a
33a - 66b
33(a-2b)
so the largest integer that must be a factor of the above eq. is 33

IMO D

BenjaminS · Answer

I assume that when m = xy , n = yx. 
x and y is the digit.
So m = 10*x+y and n = 10*y+x

Therefore, the question asks about 4m - 7n.
4*(10x+y) - 7*(10y+x) = 40x+4y-70y-7x = 33x-66y

33(x-2y)  is the result of 4m - 7n.

So the largest integer that must be a factor of 4m - 7n is 33

I choose D.

Posted from my mobile device

Thekingmaker · Answer

i didn't carry out such elaborate calculations i just gave out a small trial test there's always the standard derivation you can consult if you weren't able to figure out the right method and time is running approximation is the key 73 and 37 was the numbers when calculated 4m-7n ~33 hence imo C

Crytiocanalyst · Answer

Let x and y be the tens and unit digit of m ,

=>4* (10x+y) -7*(10y+x)
=>33*x -66*y 
=>33(x-2y)

THerefore IMO D

A_Nishith · Answer

Why cant 33*3= 99 be the greatest factor?

Bunuel · Answer

It could. However, 99 will not ALWAYS be a factor of 4m - 7n, and since the question asks "What is the largest integer that MUST be a factor of 4m - 7n?", 99 is not correct.

HOT Competition 27 Aug/8AM: When the digits of two-digit positive inte

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