In a certain math class, one-tenth of the students cheated on a test

Question

In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught. What fraction of the class cheated on the test?

A. 21/100
B. 1/10
C. 1/8
D. 3/10
E. 4/5

mbhatt · Answer

10% cheated and got caught
20% Cheated did not get caught
so, total 30% cheated=3/10 is the answer

origen87 · Answer

Say there are 100 students and 'x' of them cheated
So the que basically asks what is x/100?

one-tenth of the students cheated on a test and were caught 
1/10 *(100)-cheated and caught-1
but one-fifth of the students who cheated did not get caught
so 4/5x of the students cheated and were caught-2

Equating 1 and 2
10=4/5x
x=50/4

x/100=1/8

Ans:C

BrentGMATPrepNow · Answer

TOTAL number of cheaters = ( # of people who cheated AND got caught ) + ( # of people who cheated AND DID NOT get caught )

To make things easier, let's say there are 100 people in the math class. 
Let x = TOTAL number of cheaters

one-tenth of the students cheated on a test and were caught  
1/10 of 100 = 10, so  10 people cheated AND got caught

one-fifth of the students who cheated did not get caught  
In other words, 1/5 of x = number of students who cheated and DID NOT get caught
Rewrite as:  0.2x = number of students who cheated and DID NOT get caught

Plug all values into original equation: TOTAL number of cheaters = ( # of people who cheated AND got caught ) + ( # of people who cheated AND DID NOT get caught )
We get; x =  10  +  0.2x 
Subtract 0.2x from both sides: 0.8x = 10
Solve: x = 12.5

What fraction of the class cheated on the test?  
If there are 100 people in the class, and 12.5 of them cheated, then the fraction of the class who cheated on the test = 12.5/100 = 1/8

Answer:  C

Cheers,
Brent

mohshu · Answer

lets say total number of students = X.
1/10 of X were cheated and caught..

let say y cheated,,, 4/5 of y cheated and were caught..

(1/10) of X = 4/5 of Y

Y/X = 1/8

ans C

ishoy · Answer

Using pick numbers, assume 120 students total.

120 * 10% cheated and got caught = 12 students
1/5 of students who cheated did not get caught so 4/5 of students who cheated got caught
12 students = 4/5 * total cheaters = 15 total cheaters
15/120 = 1/8 were cheaters

Answer C

ScottTargetTestPrep · Answer

We can let the number of students in the class be 80, so 8 students cheated and were caught. However, since 1/5 of the students who cheated were not caught, the 8 students who were caught must represent 4/5 of students who cheated. Thus if we let n = number of students who cheated, we have: We can let n = the total number of students who cheated n/10 cheated and were caught, so 9n/10 were not caught.

(4/5)n = 8

n = 10

Therefore, 10 out of 80 students cheated, which is 10/80 = 1/8 of the class.

Answer: C

Kinshook · Answer

In a certain math class, one-tenth of the students cheated on a test and were caught but one-fifth of the students who cheated did not get caught.

What fraction of the class cheated on the test?

Let x be the fraction of students who cheated on the test.

The students cheated on a test and were caught = 1/10
The students who cheated did not get caught = x/5
The students who cheated and got caught = 4x/5

4x/5 = 1/10
x= 1/8

IMO C

In a certain math class, one-tenth of the students cheated on a test

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a certain math class, one-tenth of the students cheated on a test

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards