divelab/Sys2Bench huggingface dataset:
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/8%
B)33 9/3%
C)33 1/3%
D)93 1/3%
E)33 2/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: C
Question: |x+3| – |4-x| = |9+x| How many solutions will this equation have?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: You have |x+3| - |4-x| = |8+x|
First, look at the three values independently of their absolute value sign, in other words:
|x+3| - |4-x| = |8+x|
(x+3) - (4-x) = (8+x)
Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.
when x=-10
I.) (x+3)
(-10+3)
(-7)
II.) (4-x)
(4-[-10]) (double negative, so it becomes positive)
(4+10)
(14)
III.) (8+x)
(8+-10)
(-2)
In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.
Here is how I do it step by step.
I.) |x+3| - |4-x| = |8+x|
II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:
(x+3)
x=-3
(-3+3) = 0
(4-x)
x=4
(4-4) = 0
(8+x)
x=-8
(8+-8) = 1
B
Answer: B