If a + b= 200 and a < b, is a + b > c + d?

[Jellie]

If a + b= 200 and a < b, is a + b > c + d?


(1) c + d < 200
(2) b + c + d = 300

I started out by substituting 200 into the question...so is 200 > c+d.
Then I set up an AD BCE grid. Statement 1 says that c+d is less than 200, so that's sufficient.

But then statement 2 is where I got confused. The answer is D, which means that you should be able to answer the question based on what they give you, but I don't understand how you can determine whether a+b is greater than c+d.

[divya]

If a + b= 200 and a < b, is a + b > c + d?


(1) c + d < 200
(2) b + c + d = 300

it is given a+b = 200, a < b , is a+b > c+d
rephrase the question
we know a+b = 200, so
is 200 > c+d or is c+d < 200 ? This is a YES/NO question

1. c+d < 200 ( Sufficient )
2. b + c +d = 300 - eq 1
add a to both the sides
a + b + c + d = 300 + a
we know a + b = 200, so
200 + c + d = 300 + a
c + d = a + 100
Now we know that a < b , a was equal to b a would be 100 and b would be 100, thus since a < b, a < 100
therefor a + 100 < 200 and c + d < 200 -- > Sufficient

Answer D

[Raj]

Very neat Divya. I like the way you deduced that when a+b = 200 and b >a, then b > 100. Subtle.. important observation. I missed that on my first take on this problem.

-Raj.

If a + b= 200 and a < b, is a + b > c + d?


(1) c + d < 200
(2) b + c + d = 300

it is given a+b = 200, a < b , is a+b > c+d
rephrase the question
we know a+b = 200, so
is 200 > c+d or is c+d < 200 ? This is a YES/NO question

1. c+d < 200 ( Sufficient )
2. b + c +d = 300 - eq 1
add a to both the sides
a + b + c + d = 300 + a
we know a + b = 200, so
200 + c + d = 300 + a
c + d = a + 100
Now we know that a < b , a was equal to b a would be 100 and b would be 100, thus since a < b, a < 100
therefor a + 100 < 200 and c + d < 200 -- > Sufficient

Answer D

[Guest]

thanks divya

[RonPurewal]

If a + b= 200 and a < b, is a + b > c + d?


(1) c + d < 200
(2) b + c + d = 300

it doesn't seem that statement 1 is causing any major consternation here, so let's skip to statement 2.

note that the expression c + d appears in the question prompt. therefore, solve for this expression in statement 2: c + d = 300 - b.
now, substitute this into the question prompt, and also substitute a + b = 200:
is 200 > 300 - b ?
rephrase by solving --> is b > 100?

thus, it still comes down to divya's observation that b must be more than 100, because it's the larger one of two numbers that add to 200 and therefore must be greater than half of 200.
but if you rephrase the question in this way, it's much more clear that you actually have to think about whether b > 100.
divya's solution is ingenious, but remember that ingenious is what we don't want; we want reliable and easily generalized. therefore, while i wouldn't expect you to come up with divya's awesome observation completely at random, i would expect you to come up with the following TAKEAWAY:
takeaway: if 2 numbers add up to n, then the larger number is more than n/2, and the smaller number is less than n/2.

good stuff