A stationery store sells pens and pencils. If the price of each item

Question

A stationery store sells pens and pencils. If the price of each item is expressed as a non-zero whole number of cents, how much do 5 pencils cost?

(1) 5 pencils and 3 pens cost 30 cents.
(2) 4 pencils and 4 pens cost 32 cents.

(1) 5 pencils and 3 pens cost 30 cents.

(2) 4 pencils and 4 pens cost 32 cents.

Bunuel · Accepted Answer

A stationery store sells pens and pencils. If the price of each item in cents has a positive integer value, how much do 5 pencils cost? 
 
(1) 5 pencils and 3 pens cost 30 cents.
 
This implies  5x+3y=30 . This equation has only one positive integer solution:  x=3  and  y=5 , so the price of 5 pencils is  5*3=15  cents. Sufficient.
 
(2) 4 pencils and 4 pens cost 32 cents. 
 
This implies  4x+4y=32 , which gives  x+y=8 . This equation has more than one positive integer solution, for example:  x=1  and  y=7  or  x=3  and  y=5 . Not sufficient.

Answer: A

lacktutor · Answer

A stationery store sells pens and pencils. If the price of each item is expressed as a non-zero whole number of cents, how much do 5 pencils cost?

(Statement1):
 5* pencil + 3*pen= 30 cents 
—> only 5*3 + 3*5 = 30 satisfies the equation in which pencil costs 3 cents and pen costs 5 cents
Sufficient

(Statement2): 
4*pencil + 4*pen= 32
pencil + pen= 8
—> could be 4 +4=8 or 5 +3=8 and so on 
Insufficient

The answer is A

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LevanKhukhunashvili · Answer

let express the cost of the pen - x
and cost of the pencil - y

1) stm --> 5x+3y=30; y should be multiple of five and none of the variables can be 0; 5 is the only integer which satisfies the equation, the next multiple of five is 10 and it's not valid as x must be 0 at that case.  Sufficient

2) 4x+4y=32; 4(x+y)=32; x+y=8, many pairs are possible.  Insufficient

Imo
Ans:  A

Papist · Answer

This is a classic C trap question. Let x = the cost of a pencil and y = the cost of a pen.

S1: We can write this as 5x+3y = 30. At first glance it may look unsolvable because there are two variables; however, there is only one solution since the prompt said we can only use "non-zero whole numbers", i.e. integers. This equation only works when x=3 and y=5; therefore 5x = 15. SUFFICIENT.

S2: We can write this as 4x + 4y = 32 and then simplify it to x + y = 8. There are many possible values of x. INSUFFICIENT.

ANSWER: A

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  Let us assume the cost of each pen and pencil be x and y cents  
 Where x and y are positive integers (non-zero whole numbers) 
  We are asked the value of 5y or the value of y

Statement 1:   5 pencils and 3 pens cost 30 cents
  According to this question,  3x+5y=30  
 We might think that this is one equation with two variables and thus not solvable. But the concept of special equation comes here. 
 ⇒y=\frac{30-3x}{5} 
 ⇒y=6-\frac{3x}{5}  
 The only possible value of x here is  x=5 . Thus,  y=6-\frac{3x}{5}=6-\frac{3	imes 5}{5}=6-3=3  
 Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2:   4 pencils and 4 pens cost 32 cents 
  According to this statement,  4x+4y=32 
 ⇒y=\frac{32-4x}{4}⇒y=8-x  
 Here, multiple values of  x=1,2,3,4,5,6  and  7  are possible and corresponding different values of y 
 Thus,  statement 2 alone is not sufficient

Hence the right answer is    Option A

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A stationery store sells pens and pencils. If the price of each item

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