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Comment on N=5314+k
Hi Brent I noticed a easier
Since the possible values of k is evenly spread. The sum for each of N term will be greater by 1. So if the value of the second Nth term is divisible by 3 then we know the next one divisible by 3 will be the 5th Nth term. So for 4 it will be every 4th Nth term.
So this way we could save time in solving the question.
That certainly works. Good
That certainly works. Good thinking!
Hi Brent,
Can you please explain the logic behind the solution of this problem?
https://gmatclub.com/forum/each-entry-in-the-multiplication-table-above-is-an-integer-that-is-eit-305983.html
I do not understand this part:
Statement 2 says , c =f
a*c = f
a*c = c
c*(a-1) = 0
Now a can be equal to 1 or c can be equal to 0 .
So a can be equal to 1 or a may not be equal to 1 .
Not sufficient.
Together ,
c *(a-1) = 0
From statement h not equal to zero means c is not equal to zero.
If c is not equal to zero then (a-1) = 0 ( As we can divide the zero by c which is a non zero quantity )
Hence , a = 1
Thanks
Question link: https:/
Question link: https://gmatclub.com/forum/each-entry-in-the-multiplication-table-above-...
STATEMENT 2: c = f
From the table we can see that ac = f
Since c = f, we can take ac = f, and replace f with c to get: ac = c
Subtract c from both sides to get: ac - c = 0
Factor: c(a - 1) = 0
Since the product of c and (a - 1) equals 0, we know that EITHER c = 0, OR a - 1 = 0
In other words, c = 0 OR a = 1
So one possible scenario is that c = 0 and a = 5 (since it satisfies the equation c(a - 1) = 0)
Another possible scenario is that c = 0 and a = 4 (since it satisfies the equation c(a - 1) = 0)
Since the variable a can have different values, statement 2 is not sufficient.
COMBINED STATEMENTS
Statement 1 tells us that h ≠ 0
Since the table tells us that cb = h, we now know that cb ≠ 0
If cb ≠ 0, we know that c ≠ 0 and b ≠ 0
From statement 2, we concluded that c = 0 OR a = 1
Since we now know that c ≠ 0, we can be certain that a = 1
As such, the combined statements are sufficient
Does that help?