GMAT Club Olympics 2024 (Day 2): Out of 45 chefs judging desserts, 25

Question

Out of 45 chefs judging desserts, 25 liked crème brûlée and 30 liked éclairs. How many chefs liked both desserts?

(1) Three times as many chefs liked both desserts as those who did not like either of the desserts.

(2) 5 chefs did not like either of the desserts.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Bunuel · Accepted Answer

Out of 45 chefs judging desserts, 25 liked crème brûlée and 30 liked éclairs. How many chefs liked both desserts?

{Total} = {crème brûlée} + {éclairs} - {both} + {neither}

45 = 25 + 30 - both + neither

{both} - {neither} = 10

(1) Three times as many chefs liked both desserts as those who did not like either of the desserts.

This means:

{both} = 3 * {neither}

Substituting into the previous equation:

3 * {neither} - {neither} = 10

{neither} = 5

{both} = 3 * {neither} = 15.

Sufficient.

(2) 5 chefs did not like either of the desserts.

This means:

{neither} = 5

Substituting into the previous equation:

{both} - {neither} = 10

{both} - 5 = 10

{both} = 15

Sufficient.

Answer: D.

KshtriyaNaveen · Answer

Given that ,

Total desert = 45
 
 Total people liked rème brûlée  (R) = 25,

Total people like  éclairs (E) = 30.

Asked to find who liked Both R & E(C).

Total people who don't like any desert ( N ) = N?( not given in the quesiton )

This quesiton resemeble venn diagram scenario, By using veen diagram we can solve this quesiton in easier way.

Total desert = R + E - C + N  -> Equation 1

statement 1: Three times as many chefs liked both desserts as those who did not like either of the desserts.

given C = 3N 
 
 By keeping this value in equaiton 1, we can get value of C. Therfore statement 1 is corrrect , So possible answer is A & D.

Statement 2:  5 chefs did not like either of the desserts.

Given N = 5, by substuting this value in eqution 1, we can find value of c , so Statement 2 is correct.

Therefore Option D is correct answer

Kinshook · Answer

Given:  Out of 45 chefs judging desserts, 25 liked crème brûlée and 30 liked éclairs.
Asked: How many chefs liked both desserts?

crème brûlée  No crème brûlée  Total ​​​​​​​ 
  éclairs  x= ?    30  
  No éclairs      45-30=15  
  Total   25  45-25=20  45  
 (1) Three times as many chefs liked both desserts as those who did not like either of the desserts.
 
    crème brûlée ​​​​​​​ No crème brûlée ​​​​​​​ Total ​​​​​​​ 
  éclairs  x  30-x  30  
  No éclairs  25-x=15-x/3  x/3  15  
  Total   25  20  45  
 
25-x = 15-x/3
2x/3 = 10
x = 15
The number of chefs who liked both desserts = x = 15
SUFFICIENT

(2) 5 chefs did not like either of the desserts. 
    crème brûlée ​​​​​​​ No crème brûlée ​​​​​​​ Total ​​​​​​​ 
  éclairs  x=25-10=15    30  
  No éclairs  15-5=10  5  15  
  Total   25  20  45  
 
The number of chefs who liked both desserts = x = 15
SUFFICIENT

​​​​​​​IMO D

Oppenheimer1945 · Answer

A+B+X+Y=45
A+X=25
B+X=30

What is X?

S1) gives rel b/w X&Y, we have 3 linear eq with 3 variables, solving will get X (Suff)

S2) gives y=5, again we have 3 linear eq with 3 variables, solving will get X (Suff)

D)

Jolex · Answer

There are 45 chefs in total.
25 chefs liked cremebrulee.
30 chefs liked eclairs.

We need to find the number of chefs who liked both desserts. We'll use the principle of set theory and the principle of inclusion-exclusion for this.

Statement 1: Three times as many chefs liked both desserts as those who did not like either of the desserts.

First, let's set up the equation using the principle of inclusion-exclusion

Total chefs=(Chefs who liked creme brulee) +(Chefs who liked eclairs) −(Chefs who liked both) +(Chefs who liked neither)
45=25+30−C+N

Where C is the number of chefs who liked both desserts, and N is the number of chefs who did not like either dessert.

According to Statement 1:C=3N

Substitute C=3N into the inclusion-exclusion equation:
45=25+30−3N+N
45=55−2N
2N=55−45
2N=10
N=5

So C=3N=3×5=15.

Therefore, Statement 1 alone is sufficient to determine that 15 chefs liked both desserts.

Statement 2: 5 chefs did not like either of the desserts.

This statement directly gives us: N=5

Using the inclusion-exclusion equation again:
45=25+30−C+5
45=55−C+5
45=60−C
C=60−45
C=15

Therefore, Statement 2 alone is also sufficient to determine that 15 chefs liked both desserts.

Conclusion:
Both statements independently provide sufficient information to determine the number of chefs who liked both desserts. Hence, the answer is:

D. EACH statement ALONE is sufficient to answer the question asked.

smile2 · Answer

Let's fill the 2x2 matrix

Let's say, we notate as below 
Like Creme Brulee = LCB
Do not Like Creme Brulee = DLCB
Like Eclairs = LE
Do not Like Eclairs = DLE

LCB           DLCB

LE                ?                                  30

DLE                                              15
 
 Total        25                 20           45

With this skeleton, let's jump into statement 1,

LCB           DLCB

LE               3x              y               30

DLE             3x             x                15
 
 Total          25            20               45

meaning, 3x + y = 30 and x + y = 20, then 2x = 10, x = 5. Therefore, statement 1 alone is sufficient

let's jump into statement 2,

LCB           DLCB

LE               15            15             30

DLE             10             5              15
 
 Total          25            20              45

Therefore, statement 2 alone is sufficient.

In total, D is the right answer choice as each statement individually is sufficient to answer number of chefs who liked both desserts.

OmerKor · Answer

Hello, everyone. This is the second day of the competition. I truly like the concept of competitiveness. Every day is new. Everything can change. To win, you must maintain a consistent pace. Get ready. Here we GO. Let's get started with our explanation for this topic on day two: Analyze the Question&Answer Choices: Question : First, let's look at the question. We are dealing with kind of OverLapp kind of DoubleMatrix problem. Reading and Understanding the question: Given : | Creme | No Creme | Total ------------------------------------------------------- eclairs | | | 30 ------------------------------------------------------- No eclairs | | | 15 ------------------------------------------------------- Total | 25 | 20 | 45 I tried to creat a table sheet

NOW, After Reading and Understanding we can move to the Statements

Solving: (1) Creme AND elcair = 3 No Creme AND No elcair 3x = x lets put it in our double matrix table: (this is why I invested in building it

) Given : | Creme | No Creme | Total ------------------------------------------------------- eclairs | 3x | | 30 ------------------------------------------------------- No eclairs | 25-3x | x | 15 ------------------------------------------------------- Total | 25 | 20 | 45 => 25-3x + x = 15 2x=10 x=5 We have out Answer: 3x=15 SUFFICIENT (2) No Creme AND No elcair = 5 We can directly infer that this is the same table with 5. but because I already built such an amazing table we will use it

(and for those who want to elaborate of course) lets put it in our double matrix table: | Creme | No Creme | Total ------------------------------------------------------- eclairs | 15 | | 30 ------------------------------------------------------- No eclairs | 10 | 5 | 15 ------------------------------------------------------- Total | 25 | 20 | 45 SUFFICIENT Our Answer is D https://cdn.gmatclub.com/cdn/files/forum/images/smilies/1f642.png THE END I hope you liked the explanation, I have tried my best here. Let me know if you have any questions about this question or my explanation. https://cdn.gmatclub.com/cdn/files/forum/images/smilies/1f44f-1f3fb.png

GMAT Club Olympics 2024 (Day 2): Out of 45 chefs judging desserts, 25

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	crème brûlée	No crème brûlée	Total
éclairs	x= ?		30
No éclairs			45-30=15
Total	25	45-25=20	45

GMAT Data Sufficiency (DS) Questions

GMAT Club Olympics 2024 (Day 2): Out of 45 chefs judging desserts, 25

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