At a carnival, how many people are currently waiting for the Ferris

Question

At a carnival, how many people are currently waiting for the Ferris wheel?

(1) If an equal number of people were waiting for the Ferris wheel in 3 lines, 2 would be left over.
(2) If an equal number of people were waiting for the Ferris wheel in 4 lines, 1 would be left over.

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Adit_ · Answer

Statement 1:
3x+2 form
INSUFFICIENT

Statement 2:
4y+1 form
INSUFFICIENT

Combining thw two:
3x+2=4y+1
Two variables cant be solved for.
INSUFFICIENT

Answer:  Option E

Dereno · Answer

How many people wait for the Ferris wheel ?

Statement 1:

If an equal number of people were waiting for the Ferris wheel in 3 lines, 2 would be left over.

Equal number can be anything from 1 to positive infinity.

So, N = 3x +2

Hence,  Insufficient

Statement 2:

If an equal number of people were waiting for the Ferris wheel in 4 lines, 1 would be left over.

Equal number can be anything from 1 to positive infinity.

So, N = 4y +1

Hence,  Insufficient

Combining both statements 1 and 2, we get

3x+2 = 4y+1

At x=1=y, then the number of people waiting for Ferris wheel is 5.

Then, the value coincides for x in increments of 4, and for y increments of 3. That’s at x=5 , and y=4.

The values of number of people waiting for Ferris wheel is not unique.

Hence,  Insufficient

Option E

chloreton · Answer

One thing I have noticed in these types of remainder questions is that, when the constraints are not given option  E  is almost always right.

Had they given a constraint like no of people donot exceed 10, then we can do the calc as below and arrive at option  C 
3x+2 (2, 5 ,8,11..)
4y+1(1, 5 ,9,13..)

Thanks

ExpertsGlobal5 · Answer

Explanation:  
 
Let the total number of people currently waiting for the Ferris wheel be N.
  We need to find whether the value of N can be determined.  
 
 Statement (1) 
 
N = 3p + 2, where p is some non-negative integer. (Equation I)
 
 Possibility 1:  If p = 1, then N = 5.
 Possibility 2:  If p = 2, then N = 8.
 
It is NOT possible to determine with certainty the value of N.   Hence, Statement (1) is insufficient   . 
 
 Statement (2) 
 
N = 4q + 1, where q is some non-negative integer. (Equation II)
 
 Possibility 1:  If q = 1, then N = 5.
 Possibility 2:  If q = 2, then N = 9.
 
It is NOT possible to determine with certainty the value of N.   Hence, Statement (2) is insufficient   . 
 
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements. 
 
 Statement (1) and Statement (2) combined  
 
N = 5 is the first common term that satisfies both Equation I and Equation II.
Also,   any value of the form “k x LCM(3,4) + First common term”  , such as 17, 29, and 41 will also   satisfy both Equation I and Equation II  .
 
It is NOT possible to determine with certainty the value of N.   Hence, Statement (1) and Statement (2) combined are insufficient.  
 
  E is the correct answer choice.

At a carnival, how many people are currently waiting for the Ferris

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GMAT Data Sufficiency (DS) Questions

At a carnival, how many people are currently waiting for the Ferris

Prep Toolkit

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

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Perfect 805 Score Debrief by Julia

My Rewards