Each of the 30 first graders in a class bought one of three kinds of d

Hi,

From our original question stem, we know that each of the 30 students bought one dictionary. That is, 30 dictionaries were bought so we can write
"pocked + compact + ordinary = 30" --> p + c + o = 30.
Statement (1) tells us that a total of $540 was spent on all dictionaries. Since we know the price of each of the dictionaries, we can use the same notation as above to write this as:
15p + 18c + 20o = 540. (That is, the number of pocket dictionaries * $15 + the number of compact * $18 + the number of ordinary * $20 = $540)
Since every student bought exactly one dictionary, statement (2) tells us that there are twice as many pocket dictionaries as compact dictionaries.
This translates into p = 2c.

So in total we now have 3 equations:
p + c + o = 30
15p + 18c + 20o = 540
p = 2c

Since these are 3 (different) equations with 3 variables they have 1 solution and we can mark (C), if we like we can solve explicitly:
p+c+o=30 --> 2c+c+o=30 --> o=30 - 3c
15p + 18c + 20o = 540--> 30c + 18c + 20(30 - 3c) = 540 --> 12c = 60 --> c = 5
So 5 students bought compact dictionaries.

Hope that helps!

IMO C.

Say if number of students with PE=x, CE=y, OE=z, then the question stem asks y=?. Given: x + y + z=30.

1) 15x + 18y + 20z= 540 & we are given that x + y + z=30. Not Sufficient.

2) x=2y. 2y + y + z=30. 3y + z=30. Not Sufficient.

Combining 1) and 2), we get 30y + 18y + 20z=540 & 3y + z=30. Sufficient.

[quote="urvashis09"]IMO C.

Say if number of students with PE=x, CE=y, OE=z, then the question stem asks [b]y=?[/b]. Given: x + y + z=30.

1) 15x + 18y + 20z= 540 & we are given that x + y + z=30. [b]Not Sufficient.[/b]

2) x=2y. 2y + y + z=30. 3y + z=30. [b]Not Sufficient.
[/b]
Combining 1) and 2), we get 30y + 18y + 20z=540 & 3y + z=30. [b]Sufficient.[/b][/quote]


Just to add when we combine two statements we actually have two values for equation

48x+ 20y=540
Y=3 x=10 (1)
Y=15 x=5. (2)

But in total in first (1) becomes 3x+y=33. (3x because x for compact and 2x for PE)
Total in (2)=3x+y=30

Only 2nd so C is answer

Give kudos if it helps

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