If a certain store has fewer than 40 pumpkins, how many pumpkins does

Question

If a certain store has fewer than 40 pumpkins, how many pumpkins does the store have?

(1) If 8 customers bought an equal number of pumpkins, 3 would be left over.
(2) If 6 customers bought an equal number of pumpkins, 1 would be left over.

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nsd24 · Answer

8x + 3 < 40

Here x can have these values, i.e. 1, 2, 3, 4
Not 5, because 8 x 5 = 40 + 3 = 43 is not less than 40. Hence, we cannot find specific number of pumpkins.
Information 1 is insufficient.

Similarly,
6x + 1 < 40

Here too x can have many values i.e. 1, 2, 3, 4, 5, 6
Hence, Information 2 is insufficient.

Together,
We can say from Information 1 that when we make groups of 6 pumpkins, 1 is left out. Now I want to make groups of 8 pumpkins in a way that 3 are left out. If I imagine taking 2 pumpkins from the groups of 6 and adding them to other grps to make them 8, this can be done in following ways

When groups exist in - 6 6 6 1 -> 8 8 Rem = 2+1 = 3
In this case total pumpkins = 19 -> acceptable

When groups exist in - 6 6 6 6 6 6 6 1 -> 8 8 8 8 8 Rem = 2+1 = 3
In this case total pumpkins = 43 - > not acceptable

Hence, both information together are sufficient. Imo Option C.

Adit_ · Answer

Its fun to work out something more in such question 
Eventual equation we get combining the 2 is:
3y-4x=1
y=3,7,11.. all the integer equations forming an AP with d=4
In this case 3 is the only one that leads to a value under 40 (skipped all calculation which is brief in itself 6y+1=8x+3)

We thus get 19 as our answer.
C is the answer.

Dereno · Answer

It’s mentioned we have fewer than 40 pumpkins. We need to find the number of pumpkins in store.

Statement 1:

If 8 customers bought an equal number of pumpkins, 3 would be left over.

8a + 3 = Total number of pumpkins.

8a+3 < 40

The possible values are : 11,19,27,35.

We have more than one value. Hence,  Insufficient

Statement 2:

If 6 customers bought an equal number of pumpkins, 1 would be left over.

6b + 1 <40

The possible values are : 7, 13, 19, 25, 31,36.

We have more than one value. Hence,  Insufficient

Combining both, we get

The common value among the two groups is  19 .

Hence,  Sufficient

Option C

ExpertsGlobal5 · Answer

Explanation:  
 
Let the total number of pumpkins be N.
Since the store has fewer than 40 pumpkins, N < 40. (Equation I)
  We need to find whether the value of N can be determined.  
 
 Statement (1) 
 
N = 8p + 3, where p is some non-negative integer. (Equation II)
 
 Possibility 1:  If p = 1, then N = 11.
 Possibility 2:  If p = 2, then N = 19.
 
It is NOT possible to determine with certainty the value of N.   Hence, Statement (1) is insufficient   . 
 
 Statement (2) 
 
N = 6q + 1, where q is some non-negative integer. (Equation III)
 
 Possibility 1:  If q = 1, then N = 7.
 Possibility 2:  If q = 2, then N = 13.
 
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  
 
The values of N that satisfy both Equation I and Equation II are 3, 11,   19  , 27, and 35.
The values of N that satisfy both Equation I and Equation III are 1, 7, 13,   19  , 25, 31, and 37.
The only value of N that satisfies all three equations is   19  .
 
It is possible to determine with certainty the value of N.   Hence, Statement (1) and Statement (2) combined are sufficient.  
 
  C is the correct answer choice.

If a certain store has fewer than 40 pumpkins, how many pumpkins does

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GMAT Data Sufficiency (DS) Questions

If a certain store has fewer than 40 pumpkins, how many pumpkins does

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

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