M47-104

Question

Formatted question: At a print shop, premium brochures cost $14 each and standard flyers cost $9 each. For an event, Nora ordered only premium brochures, and Eli ordered only standard flyers. How many premium brochures did Nora order?

(1) If Nora had ordered as many premium brochures as Eli ordered standard flyers, Nora’s order would have cost $45 more than Eli’s order.
 
(2) If Nora had ordered standard flyers instead, in the same quantity as the premium brochures she actually ordered, her total cost would have been $35 less.

Bunuel · Answer

Official Solution:

At a print shop, premium brochures cost $14 each and standard flyers cost $9 each. For an event, Nora ordered only premium brochures, and Eli ordered only standard flyers. How many premium brochures did Nora order? 
 
Let  p  be the number of premium brochures Nora ordered, and let  s  be the number of standard flyers Eli ordered.
 
Then Nora’s total cost was  14p  dollars, and Eli’s total cost was  9s  dollars.
 
(1) If Nora had ordered as many premium brochures as Eli ordered standard flyers, Nora’s order would have cost $45 more than Eli’s order.
 
If Nora had ordered as many premium brochures as Eli ordered standard flyers, then that hypothetical order would have cost  14s  dollars, while Eli’s actual order cost  9s  dollars.
 
So (1) gives:
 
 14s - 9s = 45 
 
 s = 9 
 
This determines only how many standard flyers Eli ordered. It does not determine  p . Not sufficient.
 
(2) If Nora had ordered standard flyers instead, in the same quantity as the premium brochures she actually ordered, her total cost would have been $35 less.
 
If Nora had ordered standard flyers instead, in the same quantity, then her cost would have been  9p  dollars instead of  14p  dollars.
 
So (2) gives:
 
 14p - 9p = 35 
 
 p = 7 
 
This determines the number of premium brochures Nora ordered. Sufficient.
 
Answer: B

horrorslive · Answer

Bunuel  doesnt it mean from the first statement that p=s. Since Nora orders as many brochures as Eli ordered standard flyers? 
So shouldn't each statement alone be sufficient?

Bunuel · Answer

Statement (1) does not say that Nora actually ordered the same number of brochures as Eli ordered flyers.

It says that  if Nora had ordered  that quantity, her order would have cost $45 more. So this is a hypothetical situation based on Eli’s quantity, not a statement that  p = s .

That is why statement (1) determines Eli’s quantity, but not Nora’s actual quantity.

okgmat · Answer

does the second one also not say  'had ordered' ?

Bunuel · Answer

Yes, statement (2) also says “had ordered,” but the hypothetical is different.

In statement (1), Nora’s hypothetical quantity is Eli’s quantity, so it tells us about Eli’s order, not Nora’s actual order.

In statement (2), Nora’s quantity stays the same as her actual quantity. Only the item type changes. So it directly tells us Nora’s actual number of brochures.

That is why statement (2) is sufficient.

M47-104

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