If each of the stamps Carla bought cost 20, 25, or 30 cents and she bo

Bunuel

Is this a new GMAT prep question? I did not see in the collection in the webiste.

Carla bought at least one of each denomination. At a minimum, she has 75 cents of stamps (30, 20, 25)

(1) If she spent a total of $1.45, we already know 75 cents consists of one of each stamp.

We have 70 cents unaccounted for; she could have purchase a 30 cent stamp and 2 20 cent stamps or 2 25 cent stamps and 1 20 cent stamp. INSUFFICIENT.

(2) We have no idea what these 6 stamps consist of; INSUFFICIENT.

(1&2) The two scenarios mentioned for statement 1 still apply here. INSUFFICIENT.

Answer is E.

GMATinsight Bunuel chetan2u I don't get why we CAN distribute 20 for instance to 25y (see highlighted part above) if y has to be an INTEGER. Can you explain?

BrentGMATPrepNow can you help with ST1? I get this equation 4x+5y+6z=29 and nothing seems to work, no matter what values I plug into it.

Your equation, 4x+5y+6z=29, is correct.
Two possible solutions are:
1) x = 2, y = 3 and z = 1
2) x = 3, y = 1 and z = 2

If each of the stamps Carla bought cost 20, 25, or 30 cents and she bought at least one of each denomination, what is the number of 25-cent stamps that she bought?

(1) She spent a total of $1.45 for stamps.
(2) She bought exactly 6 stamps.



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Let # of 20 cents coins be -> x
Let # of 25 cents coins be -> y
Let # of 30 cents coins be -> z

x+y+z >=3


(1) 20x + 20y +30z =145 (1.45 *100)
Insufficient - 3 Variables 1 equation

(2) x +y +Z = 6
Insufficient - 3 Variables 1 equation


(1) & (2) combined
20x + 20y +30z =145
x +y +Z = 6

3 variables 2 equation - Insufficient

hence Answer is E

KarishmaB is this approach correct ?

Each statement alone are obviously insufficient so I'll jump directly to the part where we combine Statment I and Statement II and then check

let x be the number of 20 cents stamps
let y be the number of 25 cents stamps
let z be the number of 30 cents stamps

so, the total cost of all the stamps combined would be

20x+25y+30z

Statement (I) She spent a total of $1.45 for stamps
Statement (II) She bought exactly 6 stamps

so she spent a total of 145cents[$1.45] on the stamps and bought a total of 6 stamps

note that to get the value of 20x+25y+30z=145

y either has to be 1 or 3. Why?
because only in that case can we have 5 in the unit digit of the total cost of the stamps [145]

if y is 2 or 4 then that would make the value of y stamps either 50cents or 100cents and we can never get a value of units digit of x or z type stamps to be 5 because they cost 20cents and 30cents respectively [multiples of 10]

y obviously can't be 5 because that would either make x=0 or z=0 and it has been mentioned that she did buy at least 1 stamp of each kind

Now that we know that y is either has to be 1 or 3

case I: y=1

if y=1 then value of y stamps will be 25cents and the total value of x and z stamps will be 145-25=120cents

can we get 20x+30z=120?

yes, if x=3 and z=2 then we will have 20x=60 and 30z=60

and the total value of 20x+25y+30z=145 [60+25+60]

case II: y=3

if y=3 then value of y stamps will be 75cents and the total value of x and z stamps will be 145-75=70cents

can we get 20x+30z=70?

yes, if x=2 and z=1 then we will have 20x=40 and 30z=30

and the total value of 20x+25y+30z=145 [40+75+30]

So we have 2 cases in which the total value of the stamps can be 145cents [$1.45] and the total number of stamps can be 6

But, observe that in Case I: the number of y stamps[25cents] = 1 and in Case II: the number of y stamps[25cents] = 3

Hence, we have two different answers for the number of 25cents stamps(y), therefore, both statements together are also not sufficient

Answer Choice E