The Cyclepaths Bicycle Factory has 300 bicycles in stock. The bicycles

Question

The Cyclepaths Bicycle Factory has 300 bicycles in stock. The bicycles are either blue or red, and they come in two sizes: large and small. If 175 of the bicycles are blue, and 140 are large, how many are both blue and large?

(1) There 90 small red bicycles.

(2) There are twice as many small blue bicycles as there are large red bicycles.

chetan2u · Answer

The Cyclepaths Bicycle Factory has 300 bicycles in stock. The bicycles are either blue or red, and they come in two sizes: large and small. If 175 of the bicycles are blue, and 140 are large, how many are both blue and large?

(1) There 90 small red bicycles.
But total small are 300-140=160, so small blu cycles are 160-90=70...
If 70 blue cycles are small, remaining 175-70=105 are large..
Sufficient

(2) There are twice as many small blue bicycles as there are large red bicycles.
B=175, so R=300-175=125
L=140, so S=300-140=160
SB=2*LR, LB=??
SB+LB=B=175=SB+LB...(I)
Also LB+LR=L=140=LB+SB/2...(II)
Subtract II from I...
SB+LB-(LB+SB/2)=175-140=35.......SB/2=35.....SB=70
Therefore LB=175-70=105..
Sufficient

You can make a matrix too..
.........B......R....T
L.... X .... Y ...140
S....2Y....Z.....160
T...175...125..300
So look at the L row..
X+Y=140
Look at the B column..
X+2Y=175
So two equation, two variables.. we can find X
Sufficient

D

EgmatQuantExpert · Answer

Solution

Given:  
 • The Cyclepaths Bicycle Factory has 300 bicycles in stock
• The bicycles are either blue or red, and they come in two sizes: large and small
• 175 of the bicycles are blue, and 140 are large

To find:  
 • How many bicycles are both blue and large

Approach and Working:   
As 140 are large, 
 • Small bicycles = 300 – 140 = 160

Similarly, 175 are blue,
 • Hence, red bicycles = 300 – 175 = 125

If we assume small blue bicycles to be x, then we can say
 • Small red bicycle = 160 – x 
• Large blue bicycles = total blue – small blue = 175 – x 
• Large red bicycles = total large – large blue = 140 – (175 – x) = x – 35 
 
The following diagram gives us the detail:

https://e-gmat.com/blogs/wp-content/uploads/2018/07/bicycles.png

Hence, if we can find x, we can answer our question

Analysing Statement 1  
 • As per the information given in statement 1, there are 90 small red bicycles.
 o Or we can say, 160 – x is 90
o We can find the value of x

Hence, statement 1 is sufficient.

Analysing Statement 2  
 • As per the information given in statement 2, there are twice as many small blue bicycles as there are large red bicycles
 o Or we can say, x = 2 (x – 35)
o We can find the value of x from this equation

Hence, statement 2 is sufficient

Hence, the correct answer is option D.

Answer: D

Vidhi12 · Answer

Large 
 Small 
 total 
 
  Blue 
 x 
  
 175(given) 
 
  Red

125 
 
  total 
 140(given) 
 160 
 300

We are asked to find the value of x in the table

(1) There 90 small red bicycles.

Large   
   Small   
   total   
 
    Blue   
   x   
   let the value be "y"   
   175(given)   
 
    Red   
  
   90   
   125   
 
    total   
   140(given)   
   160   
   300

therefore y+90=160 
 y=70 
 and y+x=175, 
  70+x=175 
 and x is 105

A)1 Alone is sufficient

(2) There are twice as many small blue bicycles as there are large red bicycles.   
  let large red bicycles= L  
  thus,  
  small blue bicycles= 2L

Large   
   Small   
   total   
 
    Blue   
   175- 2L   
   2L   
   175(given)   
 
    Red   
   L   
   125- L   
   125   
 
    total   
   140(given)   
   160   
   300

175-2L+L= 140  
  L=35  
  175-2L=175-70=105

Thus D) Each statement alone is sufficient 
 Hope this helps!

The Cyclepaths Bicycle Factory has 300 bicycles in stock. The bicycles

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	Large	Small	total
Blue	x	let the value be "y"	175(given)
Red		90	125
total	140(given)	160	300

GMAT Data Sufficiency (DS) Questions

The Cyclepaths Bicycle Factory has 300 bicycles in stock. The bicycles

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