12 Days of Christmas GMAT Competition - Day 2: A car is randomly

Question

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

If a car is randomly selected from a factory's production line, what is the probability that the selected car is electric?

(1) The probability that a car selected at random is neither red nor electric is 1/3.
(2) The probability that a car selected at random is red but not electric is 2/15.

Bunuel · Accepted Answer

GMAT Club's Official Explanation:

If a car is randomly selected from a factory's production line, what is the probability that the selected car is electric?

This question is essentially about overlapping groups framed as a probability problem. We use the formula:

Total = Electric + Red - Both + Neither

Our goal is to calculate Electric/Total * 100. To make calculations easier, let's assume Total = 45 (the least common multiple of the denominators from the statements).

(1) The probability that a car selected at random is neither red nor electric is 1/3.

45 = Electric + Red - Both + 15

Not sufficient.

(2) The probability that a car selected at random is red but not electric is 2/15.

The above implies:

Red - Both = 6.

Not sufficient.

(1) + (2) Substituting Red - Both = 6 into 45 = Electric + Red - Both + 15, we get 45 = Electric + 6 + 15, which simplifies to Electric = 24. Therefore, Electric/Total * 100 = 24/45 * 100. Sufficient.

Answer: C

giuseppemvn · Answer

Q: Probability that a randomly selected car is electric.

Statement 1

First statement gives us probability of choosing a car NOT Red and NOT Electric. We can calculate the probability of selecting a car both red and electric, but it's not what the question asks. Statement 1 is not sufficient.

Statement 2

Second statement gives us probability that a randomly selected car is red and NOT Electric. Statement 2 is not sufficient for the same reason explained above.

Statement 1 + Statement 2

If we combine both informations we have P(Red, Not electric) and P(Not red, Not electric). If we sum these two we get the total probability of a car being not electric. This event and the car being electric instead are mutually exclusive and collectively exhaustive, thus:

P(E) + P(NE) = 1

So:

P(E) = 1 - P(NE)

Statement 1 + Statement 2 are sufficient.

Answer  C

hr1212 · Answer

Let R stand for red, NR for non-red, E for electric and NE for non-electric then,

Statement 1 -

R 
 NR 
 T 
 
  E

? 
 
  NE 
  
 1/3

T

1

Not sufficient

Statement 2 -

R 
 NR 
 T 
 
  E

? 
 
  NE 
 2/15

T

1

Not sufficient

Combining both these statements -

R 
 NR 
 T 
 
  E

8/15  
 
  NE 
 2/15 
 1/3 
 7/15 
 
  T

1

Answer : C

Krunaal · Answer

There are 4 possibilities Red & Electric (RE), Not Red & Electric (NRE), Not Red & Not Electric (NRNE), and Red & Not Electric (RNE)

We need to find,  (RE + NRE) / All possible cases

Statement 1

NRNE / All possible cases =  1/3 NOT SUFFICIENT

Statement 2

RNE / All possible cases =  2/15 NOT SUFFICIENT

Both Together

(NRNE / All possible cases) + (RNE / All possible cases) = 7/15

(RE + NRE) / All possible cases = 1 - 7/15 = 8/15  SUFFICIENT

Answer C.

Kinshook · Answer

If a car is randomly selected from a factory's production line, what is the probability that the selected car is electric?

(1) The probability that a car selected at random is neither red nor electric is 1/3.

Red 
 Not Red 
 Total 
 
  Electric

x=? 
 
  Not Electric 
  
 1/3 
 1-x 
 
  Total

1

The probability that the selected car is electric can not be found out with the given information.
NOT SUFFICIENT

(2) The probability that a car selected at random is red but not electric is 2/15.

Red 
 Not Red 
 Total 
 
  Electric

x=? 
 
  Not Electric 
 2/15 
  
 1-x 
 
  Total

1

The probability that the selected car is electric can not be found out with the given information.
NOT SUFFICIENT

(1) + (2)
(1) The probability that a car selected at random is neither red nor electric is 1/3.
(2) The probability that a car selected at random is red but not electric is 2/15.

Red 
 Not Red 
 Total 
 
  Electric

x=1 - 7/15 = 8/15 
 
  Not Electric 
 2/15 
 1/3 
 1-x = 2/15+1/3 = 7/15 
 
  Total

1

The probability that the selected car is electric is 8/15
SUFFICIENT

IMO C

Rex885 · Answer

Red 
 Not red

Electric

not electric

Total

Making this table is super useful in case of overlapping sets question.

St 1) Prob. neither red not electric =1/3
Prob={#favourable cases/total cases}

Red 
 Not red

Electric

not electric 
  
 y

3y

Clearly NS alone

St 2) Prob. red but not electric is 2/15

Red 
 Not red

Electric

not electric 
 2x

15x

Clearly NS alone

BUT ON COMBINING THEM

Red 
 Not red

Electric

not electric 
 2x 
 y 
 2x+y=7x

15x=3y

now 15x=3y i.e. y=5x
this implies total electric cars are 15x-7x=8x

Hence prob. of electric car = 8/15
SUFFICIENT

missionmba2025 · Answer

Red 
 Not Red

Electric

We need to find this 
 
  Non Electric

Total

1

(1) The probability that a car selected at random is neither red nor electric is 1/3.

Red 
 Not Red

Electric

We need to find this 
 
  Non Electric 
  
 1/3

Total

1

The information given is not sufficient as we can't reach to the required information. Hence, eliminate A, and D.

(2) The probability that a car selected at random is red but not electric is 2/15.

Red 
 Not Red

Electric

We need to find this 
 
  Non Electric 
 2/15

Total

1

The information given is not sufficient as we can't reach to the required information. Hence, eliminate B.

Combined

Red 
 Not Red

Electric

We need to find this 
 
  Non Electric 
 2/15 
 1/3

Total

1

We can calculate the probability of non electric vehicles. By subtracting the obtained probability, we can get the probability of electric vehicles.

Option C

nishantswaft · Answer

It is given to us that; 
 a car is randomly selected from a factory's production line  
 Then the question asks us what is the probability that the selected car is electric? 
 It is a value type of DS question.

Let's form a table.

RED 
 NOT RED 
 TOTAL 
 
  ELECTRIC

E 
 
  NOT ELECTRIC

TOTAL

T

We have to find, value of E/T?

Let’s look at statement 1; 
 The probability that a car selected at random is neither red nor electric is 1/3. 
So we can fill our table as:- 
    
 RED 
 NOT RED 
 TOTAL 
 
  ELECTRIC

NOT ELECTRIC 
  
 x

TOTAL

3x

No other information is given to us here.
 So S1 is not sufficient. 
 (Eliminate A and D)

Let’s look at statement 2; 
 The probability that a car selected at random is red but not electric is 2/15.  
 So we can fill our table as:-

RED  
  NOT RED  
  TOTAL  
 
   ELECTRIC

NOT ELECTRIC  
  2y

TOTAL

15y

No other information is given to us here.
 So S2 is not sufficient. 
 (Eliminate B)

Combining 1 and 2; we have;

RED  
  NOT RED  
  TOTAL  
 
   ELECTRIC

E=8y  
 
   NOT ELECTRIC  
  2y  
  x=5y  
  7y  
 
   TOTAL

3x=15y

3x=15y then x=5y,
Filling our table further we have;
 E=15y-7y=8y 
 and T=15y 
 So, required probability = 8/15

The answer is C.

Lizaza · Answer

This task is easiest to solve via Venn diagram (attached), because effectively the probability of selecting a type of cars is equal to its share of the total area. Let's draw all possible cars, in which we have both red and electric ones - but we need to remember that we have no information about what other types of cars are there.

The empty space around our circles effectively means neither red nor electric - hence, the two circles together make 2/3.  Insufficient .

The only-red circle (or the half-moon figure on the left, rather) is 2/15, which tells nothing about electric cars.  Insufficient .

Knowing that both circles make 2/3, and that the left half-moon makes 2/15, we are surprisingly left with the whole circle of electric cars, which is   E=\frac{2}{3}-\frac{2}{15}=\frac{8}{15} .  Sufficient .

Therefore,   the answer is C.

Purnank · Answer

lets assume E as probability of car being electric and R as probability of car being red.
We need to find - E?

1st - The probability that a car selected at random is neither red nor electric is 1/3.
(RUE)' = 1 - RUE =  \frac{1}{3} 
and, RUE = R + E - R∩E

\frac{1}{3} = 1 - R - E + R∩E 
after solving we get,

R + E - R∩E = \frac{2}{3}

Not sufficient.

2nd - The probability that a car selected at random is red but not electric is 2/15.

R - R∩E = \frac{2}{15}

Not sufficient.

Now if we combine both statements we can get E,

E + \frac{2}{15} = \frac{2}{3} 
After solving,

E = \frac{8}{15}

Answer is C.

OmerKor · Answer

Hi Everyone

Double Matrix Question: Electric No Electric Total Red No Red Total Our Answer 100% (1) No Red & No Electric = 1/3 Electric No Electric Total Red any values equal or less then 2/3 No Red Total Our Answer 100% InSuff (2) Red & No Electric = 2/15 Electric No Electric Total Red No Red any values equal or less then 2/15 Total Our Answer 100% InSuff (1)+(2) Electric No Electric Total Red No Red Total 100% Our answer: 8/15

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	Red	Not Red	Total
Electric			x=1 - 7/15 = 8/15
Not Electric	2/15	1/3	1-x = 2/15+1/3 = 7/15
Total			1

	Electric	No Electric	Total
Red		any values equal or less then 2/3
No Red		[1][/3]
Total	Our Answer		100%

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