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25 Jul 2018, 04:07
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:58) correct
34%
(02:12)
wrong
based on 372
sessions
History
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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.
(1) There 90 small red bicycles.
(2) There are twice as many small blue bicycles as there are large red bicycles.
25 Jul 2018, 04:22
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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
(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
25 Jul 2018, 23:25
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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:
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
