goyalsau wrote:Cedagmat wrote:I have a similar problem that I can't seem to make out correctly. Does anyone have any suggestions?
Steve took a math test that consists of basic questions and advanced questions. A correct answer to the basic question will gain 1 point and a correct answer to advanced question will gain 2 points. How many questions does the test consist of?
(1) Steve answered 80% of the basic question and 30% of the advanced questions correctly, and gained 88 points.
(2) There are twice as many advanced questions as the basic question.
My thinking was B = basic Questions, A = Advanced questions
(0.8)B+0.3(A) = 88
A/B = 2/1, then A = 2B; then substitution:
0.8(B) + 0.3(2B)=88
B = 62.8 which does not see like the correct answer at all? The OG is C (which I understand, I just want to make the math work).
Buddy i able to do the question, but with some slight changes.
There are twice as many advanced questions as the basic question.
{ Just change it There are twice as many Basic questions as the Advance question. }
Lets assume there were 40 basic question. then there must be 20 Advanced questions.
Total marks will be 40 * 1 + 20 * 2 = 80
Now we know that 80% basic question are correct, it means 32 marks are scored from basic questions.
and we also know 30% advanced questions are correct , it means 6 questions are correct and in total 12 marks are scored of them,
in total 44 marks are scored of 80, means 55% of total marks,
Now i know 88 is 55% of total marks, it means total marks are 160,
80 questions of basic and 40 questions of Advanced.
out of 80 -- 64 are correct means 64 points
out of 40 -- 12 are correct means 24 points.
in total 88 points.
I changed the questions. Because i was not getting the answer. From the previous question.
and please if you have the official explanation. Do share......... it ....
Hi goyalsau & Cedagmat!
Very interesting question, and goyalsau, I like that you were able to solve the answer by craftily picking numbers that happened to give the correct 88 points! But how would we solve this problem algebraically from the start (both the original and the edited version). Well, I'm going to do both, because Cedagmat is right that the math doesn't quite come out with the original but not in the way you initially said (I'll point out the calculation error you made as we go). But you end up with the student getting a fractional number of questions right (35.2 of the basic and 26.4 of the advanced, and that doesn't make sense - but just so you can check your math I'll run through it!)
ORIGINAL QUESTION
Stem:"Steve took a math test that consists of basic questions and advanced questions. A correct answer to the basic question will gain 1 point and a correct answer to advanced question will gain 2 points. How many questions does the test consist of?"
Let's organize our information:
A = # of Advanced questions on the test
2 = value of each CORRECT Advanced question
B = # of Basic questions on the test
1 = value of each CORRECT Basic question
A+B = Total # of questions on the test
What are we looking for?
A+B
Statement (1):"Steve answered 80% of the basic question and 30% of the advanced questions correctly, and gained 88 points."
If he answered 80% of the Basic questions correctly, then he answered .8(B). For each of those, he scored only 1 point. So 1 point each would be .8(B)(1).
If he answered 30% of the Advanced questions correctly, then he answered .3(A). For each of those, he scored 2 points. So 2 point each would be .3(A)(2).
[/i](notice that this is where you made your mathematical mistake Cedagmat - you forgot to count each correct Advanced as 2 points).[/i]
Adding these up, we should get the total of 88 points...
.8B + .3A(2) = 88
.8B + .6A = 88
(simplify)
8B + 6A = 880
4B + 3A = 440
But I can't get the sum of A + B, so [spoiler]NOT SUFFICIENT![/spoiler]
Statement (2):"There are twice as many advanced questions as there are basic questions."
The easiest way to set these up is the ratio:
A/B = 2/1
A = 2B
I can rewrite this as A-2B, but I can't get the SUM of A+B, so [spoiler]NOT SUFFICIENT![/spoiler]
Statement (1+2):Putting it together
4B + 3A = 440 ...AND... A = 2B
4B + 3(2B) = 440
10B = 440
B = 44
A = 2(44) = 88.
A+B = 88+44 = 132
SUFFICIENT
**BUT - here is the problem...remember that Steve got 80% of the Basic problems and 30% of the Advanced problems correct. That would be .8(44)=35.2 and .3(88)=26.4, and even though you never needed to solve for these specific values, the test wouldn't write a question that would have these exist. SO, lets use goyalsau's edits and just rework starting with Statement 2.
EDITED VERSION
Statement (2):"There are twice as many BASIC questions as there are ADVANCED questions."
The easiest way to set these up is the ratio:
B/A = 2/1
B = 2A
I can rewrite this as -2A+B, but I can't get the SUM of A+B, so [spoiler]NOT SUFFICIENT![/spoiler]
Statement (1+2):Putting it together
4B + 3A = 440 ...AND... B = 2A
4(2A) + 3A = 440
8A + 3A = 440
11A = 440
A = 40
B = 2(40) = 80.
A + B = 120
SUFFICIENT
**Now lets check the issue from the last version. Steve got 80% of the Basic problems and 30% of the Advanced problems correct. That would be .8(80)=64 and .3(40)=12. These are whole numbers and make logical sense so this is likely the way the actual test would present this question!
NICE Example you guys!! What great practice!
Hope this explanation helped!
Whit
