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During a recent evaluation

by gmatdriller » Sat Jan 11, 2014 3:15 am
During a recent evaluation, X students were given a two-question test. If of the students answered the first question correctly, and, of those students, answered the second question correctly, which of the following expressions indicates the number of students who did NOT answer both questions correctly?

(A) x / 10
(B) x / 5
(C) 5x / 7
(D) 9x / 10
(E) 9x

Can someone explain using a matrix table...
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by GMATGuruNY » Sat Jan 11, 2014 4:02 am
The problem as posted is missing crucial information.
It should read as follows:
gmatdriller wrote:During a recent evaluation, X students were given a two-question test. If 1/5 of the students answered the first question correctly, and, of those students, 1/2 answered the second question correctly, which of the following expressions indicates the number of students who did NOT answer both questions correctly?

(A) x / 10
(B) x / 5
(C) 5x / 7
(D) 9x / 10
(E) 9x
Let x=10.
Number who answered the 1st question correctly = (1/5)*10 = 2.
Of these 2 students, 1/2 also answered the 2nd question correctly:
(1/2) * 2 = 1.
Since only 1 student answered both questions correctly, the number who DIDN'T answer both questions correctly = 10-1 = 9. This is our target.

Now plug x=10 into the answers to see which yields our target of 9.

Only D works:
(9/10)x = (9/10) * 10 = 9.

The correct answer is D.
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by gmatdriller » Sat Jan 11, 2014 11:07 pm
Thanks Mitch, but here lies my problem:

I interpreted the question to mean the No of students who did not answer Q1 and Q2 correctly.

That is an intersection of the two; see my attached diagram for illustration.
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by sanju09 » Sat Jan 11, 2014 11:49 pm
gmatdriller wrote:Thanks Mitch, but here lies my problem:

I interpreted the question to mean the No of students who did not answer Q1 and Q2 correctly.

That is an intersection of the two; see my attached diagram for illustration.
With the corrected question and your grid (see attachment), 7X/10 answered both wrong and (X/10 + X/10) = X/5 answered only one wrong, this totals to 7X/10 + X/5 = [spoiler]9X/10.

Take D[/spoiler]
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by gmatdriller » Mon Jan 13, 2014 7:50 am
I get the point.

Please what is the difference between these 2 cases?

(i) Number of students who get Q1 AND Q2 wrong

(ii) Number of students who get both questions wrong
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by gmatdriller » Mon Jan 13, 2014 7:53 am
sanju09 wrote:
gmatdriller wrote:Thanks Mitch, but here lies my problem:

I interpreted the question to mean the No of students who did not answer Q1 and Q2 correctly.

That is an intersection of the two; see my attached diagram for illustration.
With the corrected question and your grid (see attachment), 7X/10 answered both wrong and (X/10 + X/10) = X/5 answered only one wrong, this totals to 7X/10 + X/5 = [spoiler]9X/10.

Take D[/spoiler]
Hi Sanju09,

How did u get the value for these colunm - 1st questions wrong AND 2bd question correct? (x/10)
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by gmatdriller » Thu Jan 30, 2014 10:19 pm
Nobody has responded to my question.

But take a look at the attached
Case1: Intersection of q1 and q2 wrong

(Case2: sum of the followings:
those who got q1 wrong, but q2 correct
those who got q2 wrong but q1 correct
those who got both questions wrong(q1 wrong, q2 wrong)

I usually get confused differentiating these 2 cases.
Can someone help clarify how to identify which of the two
cases we are asked pls?
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by Brent@GMATPrepNow » Mon Feb 03, 2014 9:14 am
gmatdriller wrote:I get the point.

Please what is the difference between these 2 cases?

(i) Number of students who get Q1 AND Q2 wrong
(ii) Number of students who get both questions wrong
These sentences have equivalent meanings.

However, the question asks us to find the number of students who did NOT answer both questions correctly.
This wording divides the population into two distinct (separate) groups:
Group A: those who answered questions 1 and 2 correctly
Group B: everyone else (i.e., those who did NOT answer both questions correctly)

The question asks for the number of students in Group B

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by Brent@GMATPrepNow » Mon Feb 03, 2014 11:18 am
gmatdriller wrote:During a recent evaluation, X students were given a two-question test. If 1/5 of the students answered the first question correctly, and, of those students, 1/2 answered the second question correctly, which of the following expressions indicates the number of students who did NOT answer both questions correctly?

(A) x / 10
(B) x / 5
(C) 5x / 7
(D) 9x / 10
(E) 9x

Can someone explain using a matrix table...
Sure, let's use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- answering the 1st question correctly or incorrectly
- answering the 2nd question correctly or incorrectly

Since we're told that there are X students altogether, we'll set up the matrix as follows:
Image

1/5 of the students answered the first question correctly,...
There are X students and 1/5 correctly answered the 1st question. In other words, X/5 students correctly answered the 1st question.
This means the sum of the top two boxes must add to X/5:
Image

... and of those students, 1/2 answered the second question correctly
Of the X/5 students who correctly answered the 1st question, 1/2 correctly answered the 2nd question.
1/2 of X/5 = X/10, so we know that X/10 students correctly answered the 1st AND 2nd question:
Image

Which of the following expressions indicates the number of students who did NOT answer both questions correctly?
Of total population of X students, X/10 students answered both questions correctly.
So, the REMAINING students did NOT answer both questions correctly.
X - X/10 = [spoiler]9X/10[/spoiler]
So, [spoiler]9X/10[/spoiler] students did NOT answer both questions correctly

Answer: D

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by vipulgoyal » Mon Feb 03, 2014 9:35 pm
I do agree with gmatdriller : let put it with example

case 1 : john gives right answer to q1 and wrong to q2
case 2 : david gives right answer to q1 and wrong ans to q1
case 3 : sara gives wrong ans to q1 and wrong ans to q2

i believe q is asking about only case 3 "for which we need no of students who gives wrong ans for q2"

NOT case1+case2+case3
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by GMATGuruNY » Tue Feb 04, 2014 6:58 am
gmatdriller wrote:Thanks Mitch, but here lies my problem:

I interpreted the question to mean the No of students who did not answer Q1 and Q2 correctly.

That is an intersection of the two; see my attached diagram for illustration.
In you grid, ??? is the answer to following question:
How many students answered NEITHER question correctly?
Meaning:
How many students did not answer Q1 correctly AND did not answer Q2 correctly?
Test papers for these students must look as follows:
Q1: incorrect
Q2: incorrect.
In your grid, ??? represents these students.

But the question stem for the posted problem asks the following:
How many students did NOT answer BOTH questions correctly?
Meaning:
How many students answered AT LEAST ONE of the two questions INCORRECTLY?
These students are composed of 3 cases:
Case 1: Q1 incorrect, Q2 correct
Case 2: Q1 correct, Q2 incorrect
Case 3: Q1 incorrect, Q2 incorrect.

Only the following case should NOT be included:
Case 4: Q1 correct, Q2 correct.
In your grid, Case 4 = x/10.
Thus, the number of students who answered at least one of the two questions incorrectly = 9x/10.
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by sanju09 » Tue Feb 04, 2014 11:00 pm
gmatdriller wrote:
sanju09 wrote:
gmatdriller wrote:Thanks Mitch, but here lies my problem:

I interpreted the question to mean the No of students who did not answer Q1 and Q2 correctly.

That is an intersection of the two; see my attached diagram for illustration.
With the corrected question and your grid (see attachment), 7X/10 answered both wrong and (X/10 + X/10) = X/5 answered only one wrong, this totals to 7X/10 + X/5 = [spoiler]9X/10.

Take D[/spoiler]
Hi Sanju09,

How did u get the value for these colunm - 1st questions wrong AND 2bd question correct? (x/10)
Take it this way, If 1/10 is the greatest denominator, then let X be 10. If 1/5 of the students answered the first question correctly, then X/5 = 10/5 = 2 is the total of the first column, so place it there. Of those 2 students, 1/2 or 1 answered the second question correctly, it means that only 1 student has answered both question correctly. Therefore, the number of students who did NOT answer both questions correctly is the remaining 9. So taking 9 as our target answer, let's plug in X = 10 in the choices, only D works. Oh, it's a repeat!
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by gmatdriller » Mon Mar 24, 2014 2:43 pm
Thanks everyone for devoting the time to clarify.

This fine distinctions could make a whole lot of difference.
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