MGMAT CAT - If 5a = 3b = 25, then 30ab =

[Guest]

Hi, I know this is a low level question but I seem to be missing something here regarding the solution. How did we get from this "Since 5a = 3b = 25" TO this "(5a)(3b) = (25)(25)"

If 5a = 3b = 25, then 30ab =

A) 50
B) 100
C) 625
D) 1000
E) 1250

Solution:
Since 5a = 3b = 25, (5a)(3b) = (25)(25) or 15ab = 625.

If we multiply both sides of this equation by 2, we get 30ab = 1250.

The correct answer is E.

Thanks

[Guest]

5a = 3b = 25

5a = 25
3b = 25

5a * 3b
(25) * (25)

Not sure if this is the "best" way but you could factor out 30ab like so

5a * 6b = 30ab
(1)(5a) * (2)(3b)

Since both 5a=25 and 3b=25

1(25) * 2(25)
25 * 50 = 1250

Cheers!

[esledge]

Nice explanation above, thanks!

The big-picture take-away to this one is spotting the fact that 5a and 3b are each factors of 30ab, as that will simplify the math.

If you didn't notice the commonality, you would do this problem the "long" way: solve for a and b individually, then construct 30ab.

5a = 25, so a = 5
3b = 25, so b = 25/3

30ab = (30)(5)(25/3) = (10)(5)(25) = 1250