auto-dealer's DS

[Night reader]

Among 95 cars - BMW & Honda in auto-dealer's shop, how many cars are not used?

(1) Of the cars which are used ones, 27 are BMW cars
(2) Of the cars which are not used ones, 35% are Honda cars

[fskilnik@GMATH]

Hi there,

Please note that 35% is 7/20 and 65% is (surely) 13/20... this helps looking for concrete examples.

Do the grid: BMW and Honda are lines; used and not-used are collumns.

(1) insufficient (clearly) and 27 is the only (BMW & Used) filled cell.

(2) a bit more tricky but...

> If x (the "not used" total cell asked) is 0 or if it is (say) 60, you can fill the whole grid accordingly to guarantee possible bifurcation.

(1+2) Insufficient. Let see with all detail!

Take x = 0 then

First line (BMW): 27 , 0, 27
Second line (Honda): 95-27, 0, 95-27
Last line (totals): 95, 0, 95 proving that x = 0 is viable.

Take x = 60 then

First line (BMW): 27, 39, 66
Second (Honda): 8, 21, 29
Last (Totals): 35, 60, 95

The answer is therefore E.

Regards,
Fabio.

[shovan85]

IMO E

[fskilnik@GMATH]

Hi, shovan!

That´s exactly what I did, with one IMPORTANT difference: I guaranteed the possibility of filling "your" diagrams with TWO non-negative different integer values for x in a sense that all the relationships in the grids are respected. (That is what I call a BIFURCATION.)

This is important because there are tricky problems where you could do as you did BUT you could NOT find numbers that would respect all requirements!

I hope I was clear!

Regards,
Fabio.

P.S.: someone could bother that 0 is not "really" acceptable, but it is easy to take another value for x (40 is ok)!

[Night reader]

Fabio and shovan, can the number of cars be non-integer? (hint---->)

[fskilnik@GMATH]

Fabio and shovan, can the number of cars be non-integer? (hint---->)

I guess not, for sure! I said non-negative integer, because I accepted ZERO non-used cars, that´s what I meant! Anyway, as I mentioned, you could use x = 40 and x = 60 to guarantee the answer is really E.

Regards,
Fabio.

[Night reader]

let's elaborate a bit more on B

[fskilnik@GMATH]

let's elaborate a bit more on B

Well, Night reader... if my concrete examples satisfied both (1) AND (2), they certainly satisfy (2) alone... what is your doubt, explicitly, please?

[Anurag@Gurome]

Among 95 cars - BMW & Honda in auto-dealer's shop, how many cars are not used?

(1) Of the cars which are used ones, 27 are BMW cars
(2) Of the cars which are not used ones, 35% are Honda cars

As already two grid methods are there, I'm explaining it algebraically.

Say,

• Number of used BMW cars = a
  Number of used Honda cars = b
  Number of non-used BMW cars = c
  Number of non-used Honda cars = d

Thus, (a + b + c + d) = 95
We need to find (c + d) = 95 - (a + b)
Therefore we need to know the value of either c and d or a and b for minimum. Knowing the value of one from each group (say, a and c) does not help to answer the question.

Statement 1: a = 27 => Not sufficient

Statement 2: d = 0.35*(c + d) => 7c = 13d
For c and d to be non-negative integer, c must be divisible by 13 and d must be divisible by 7. Possible pairs of values of c and d are (0, 0), (13, 7), (26, 14), (39, 21) and (52, 28).
=> Not sufficient

1 & 2 together: As a = 27 and total number of cars is 95, (a + c + d) cannot exceed 95. Thus possible values of c and are (0, 0), (13, 7), (26, 14) and (39, 21)

=> Not sufficient

The correct answer is E.

[shovan85]

Hi, shovan!

That´s exactly what I did, with one IMPORTANT difference: I guaranteed the possibility of filling "your" diagrams with TWO non-negative different integer values for x in a sense that all the relationships in the grids are respected. (That is what I call a BIFURCATION.)

This is important because there are tricky problems where you could do as you did BUT you could NOT find numbers that would respect all requirements!

I hope I was clear!

Regards,
Fabio.

P.S.: someone could bother that 0 is not "really" acceptable, but it is easy to take another value for x (40 is ok)!

Thanks Fabio!! I was considering different values of X but could not find

Thanks a lot. After I posted my answer I could see that from your response

[Night reader]

Among 95 cars - BMW & Honda in auto-dealer's shop, how many cars are not used?

(1) Of the cars which are used ones, 27 are BMW cars
(2) Of the cars which are not used ones, 35% are Honda cars

ok it's clear - no information about Honda cars in st(1) therefore Not Sufficient.
st(2) 35% of not used cars are the Honda => 35/100 or 7/20; 13/20 are BMW cars => out of 95 cars we can derive multiple integer values (the number of not used cars must be integer). As 95 can not be divided by 20 => there can be 20, 40, 60, and 80 not used cars, accordingly there can be 7, 14, 21, and 28 Honda cars and (20-7), (40-14), (60-21), (80-28) BMW cars. Not sufficient.
Combined st(1&2) is either Not Sufficient.
it turns out to be E.

[fskilnik@GMATH]

@shovan85: please follow this "old guy"´s suggestion: USE FRACTIONS (not decimals)! The 20 in the denominator is THE key to look for specific/concrete examples!


@Night reader: that´s it. Just another suggestion: when dealing with DS problems, do not look for ALL possible answers, because this is simply loosing FOCUS (and time, and energy). Try to BIFURCATE, that is, look for TWO different VIABLE answers (or prove this is not possible, of course)...

Regards,
Fabio.