GMATprep 2.1 Optimization problem- Can some instructors help

[mokap25]

A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?

The total price of the desk and chairs is 5,000
The company bought fewer than 20 desks

Can some instructors explain a systematic approach for solving optimization type problems, I am usually lost as to where to start on such problems.

Please explain your approach by helping solve this problem from GMAtprep 2.1 software.


Thanks for your help

Kaps

[ronwilliam62]

A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?

The total price of the desk and chairs is 5,000
The company bought fewer than 20 desks

Can some instructors explain a systematic approach for solving optimization type problems, I am usually lost as to where to start on such problems.

Please explain your approach by helping solve this problem from GMAtprep 2.1 software.


Thanks for your help

Kaps

let me try it ;
when i see such question i always pick the most easy statement first .in this question statement 2 is most easy pick coz it tell us nothing abt number of chairs .so we cant conclude anything

now for statement 2 : we have the following equation
150a + 50b = 5000.....(where " a " is no of desk bought & "b" is no of chairs bought )
solving this equation :
3a + b =100
now look for extreme situation :what if i b=46 ..we will get a =18 (a possible idea that means we bought 46 chairs and 18 desks )
now look for the other extreme :when b = 1 then a =33(possible idea ,that means we have one chair and 33 desk )
so statement 2 :we cant really conclude .
but if we combine two statement ,then we know a<20 that means 3a <60 this implies b>40 (coz 3a +b =100 )
so the answer sud be C

hope this answers all

[RonPurewal]

mokap25,
please follow the forum rules from now on. the forum rules require that you post the official answer to the problem.
we'll let this one go, but, from now on, posts that don't follow the rules will be deleted. thanks.

A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?

first, interpret the precise meanings of "sufficient" and "insufficient".
here:
YES = more than 40 chairs
NO = 40 or fewer chairs
so...
SUFFICIENT = DEFINITELY more than 40 chairs ... or, DEFINITELY 40 or fewer.
NOT SUFFICIENT = you CAN have more than 40, AND you CAN also have 40 or fewer.

it should be relatively quick to dispense with the two individual statements:

The total price of the desk and chairs is 5,000

you could have anywhere from 1 to 100 chairs. so, you could have more than 40, or not.
insufficient.

The company bought fewer than 20 desks

in this case, you could have anywhere from 1 to infinity chairs.
not sufficient.

Can some instructors explain a systematic approach for solving optimization type problems, I am usually lost as to where to start on such problems.

well, the most reliable approach is to test extreme values.

if you have the two statements together:
the total price of desks and chairs is $5000.
the GREATEST number of desks is 19, so that's 19 x $150 = $2850.
in that case, you have $5000 - $2850 = $2150 left over for chairs.
that's $2150/$50 = 43 chairs. (more than 40)

... but that's the GREATEST number of desks.
if you buy FEWER desks, you're going to get even MORE chairs (because you still have to spend a total of $5000). so, you're going to have 43 or even more chairs.
all of these possibilities are over 40, so, sufficient.

(c) overall.