If y = 80x + 36, where x is a positive integer, which of the following

Question

If y = 80x + 36, where x is a positive integer, which of the following cannot be factor of y ?

A. 3
B. 7
C. 12
D. 14
E. 24

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shivani1351 · Answer

y = 80x + 36 can also be written as y = 4(20x+9)
Hence, 4 will be a factor of y clearly.

Now, let's look at all the options, one by one:

Option A - 3
y mod 3 => (20x+9) mod 3 gives us 2x
Now, if x = 3, it is divisible by 3. Hence, 3 can be a factor.

Option B - 7
y mod 3 => 6x+2
Now, if x = 2, it is divisible by 3. Hence, 7 can be a factor.

Option C - 12
Now, 4 is already a factor of 12, and as we saw in Option A, 3 also divides 20x+9.
Hence, 12 can be a factor too.

Option D - 14
As y is divisible by 2 and 7 also divides 20x+9, 14 also divides 20x+9.
Hence, 14 can a factor as well.

Option E - 24
y = 4(20x+9)
There is no way to get a factor of 8 (2*4), because 20x+9 is always odd (20x is even and 9 is odd; Even + Odd = Odd always). So, while 4 is a factor of y, 2 which remains, does not divide 20x+9 as it is odd.

Hence, the correct answer is Option E - 24.

Hope this helps!

Dereno · Answer

y = 80x + 36, where x is a positive integer, x >0

80 can be written as 2*2*2*2*5

36 can be written as 2*2*3*3

Taking the common factors, we get 4, and the equation becomes  y = 4* (20x+9)

We need to look for options which cannot be a factor of y.

A. 3

If we take x=3, then y = 4* (20*3+9) = 4*3*(20+3)

This is divisible by 3. So 3 is a factor.

B. 7

If we put x =2, we get y = 4*(20*2+9) = 4*(49)

Then, y is divisible by 7.

C. 12

If we take x=3, then y = 4* (20*3+9) = 4*3*(20+3)

This is divisible 12. So 12 is a factor.

D. 14

If we put x =2, we get y = 4*(20*2+9) = 4*(49)

Then, y is divisible by 14.

E. 24

y = 4*(20x+9)

when divided by 24, we get

y = (20x+9)/6

Irrespective of the value of x = odd or even. The numerator is always ODD. Can never be divisible by 2.

Hence, Not a factor.

Option E

kevincan · Answer

Write 80 and 36 are products of prime numbers . 80 is 5 times 2^ 4 and 36 = 2^2 times 3^ 2.

Note that 2^3 and 2^4 are divisors of 80 but NOT of 36 and thus NOT of 80x + 36.

At this point , scan the answer choices for a multiple of 8 . Why ? If 80x + 36 is not a multiple of 8, it is not a multiple of of any positive integer that is a multiple of 8 ( e.g 24)

sujoykrdatta · Answer

y = 80x + 36 = 4(20x + 9)
Thus, y is a multiple of 4

Clearly, 20x + 9 is odd (since 20x is even for any integer x and 9 is odd)
Thus, 20x+9 cannot be divisible by 2
=> y can only be divisible by 4 and not any higher power of 2 i.e. 8, 16, etc.

If we observe the options, we see that Option E, i.e. 24 is a multiple of 8. Since y cannot be divisible by 8, y cannot be divisible by 24 either.

Answer E

Note: we can always choose values of x and make 20x+9 become divisible by 3 (if x=3) and 7 (if x=2). Since 4 is already a factor, we also have factors of 3x4 = 12, 7x4 = 28 and hence also 14.

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=D7CXIXM6jy0

If y = 80x + 36, where x is a positive integer, which of the following

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GMAT Problem Solving (PS) Questions

If y = 80x + 36, where x is a positive integer, which of the following

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