A store sells brand X pens for 5 dollars each, brand Y pens for $4 eac

Question

A store sells brand X pens for 5 dollars each, brand Y pens for $4 each and brand Z pens for $3 each. There are a total of 36 of these three types of pens in the store, the number of brand X pens is twice sum of the number of brand Y pens and brand Z pens, and the difference of the number of brand Y pens and the number of brand Z pens is 2. What is the largest possible total amount that three types of pens will be sold for?

(A) $163
(B) $159
(C) $156
(D) $148
(E) $125

(A) $163
(B) $159
(C) $156
(D) $148
(E) $125

IanStewart · Accepted Answer

There are 36 pens, and the ratio of type X to types Y+Z combined is 2 to 1, so 2/3 of the pens are type X, and we have 24 type X pens. We have 12 of type Y and Z, and since we want to maximize the number of type Y pens (type Y costs more), we want 2 more type Y than type Z pens. Since they add to 12 and differ by 2, we have 7 of type Y and 5 of type Z, and the total cost of all the pens is 5*24 + 4*7 + 3*5 which, just using units digits (all the answers end in a different thing, so we don't need to calculate anything other than the last digit) must end in 3, so $163 must be right.

Arro44 · Answer

I
5x + 4y + 3z = ?
 x + y + z = 36

II
Y + Z = 0.5 X
X + 0.5X = 36
X = 24

III
Difference between Y & Z is 2
Thus, Y = 7 & Z =5

Max price of pens = 24*5 + 7*4 + 5*3 = 120 + 28 + 15 = 163 AC A

Lampard42 · Answer

I)X+Y+Z=36;
II)X=2Z+2Y sub in above to get Y+Z=12
III)Y-Z=2

Solve II and III to get Z=5 and Y=7; sub to get X=24
Price Given for each pen type. Multiply to get 163$ IMO A

CareerGeek · Answer

Given, 
x + y + z = 36 ....... (1)
x = 2*(y + z) ....... (2)
--> 3*(y + z) = 36
--> y + z = 12
--> x = 2*12 = 24

Difference of the number of brand Y pens and the number of brand Z pens is 2
--> Possible values of (y, z) = (5, 7) or (7, 5)

Total amount = 5x + 4y + 3z
Amount is maximum (between y & z) when y is maximum --> y = 7, z = 5
Total amount = 5*24 + 4*7 + 3*5 = 120 + 28 + 15 = 163

IMO Option A

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EgmatQuantExpert · Answer

Solution 
  Given:  
 • A store sells,
 o brand X pens for $5 each
o brand Y pens for $4 each
o brand Z pens for $3 each

• Total these three types of pens in the store = 36
• The number of brand X pens is twice sum of the number of brand Y pens and brand Z pens
• The difference of the number of brand Y pens and the number of brand Z pens is 2

To find:  
 • What is the largest possible total amount that three types of pens will be sold for?

Approach and Working Out:   
 • X + Y + Z = 36 ……… (1)
• X = 2(Y + Z) …………. (2)

Substituting (2) in (1), we get,
 • 3(Y + Z) = 36 => (Y + Z) = 12 …….. (3)
• Thus, X = 36 – 12 = 24

And, we have, |Y – Z| = 2. 
 • Since, we are asked to find the largest possible amount, Y must be > Z 
• So, |Y – Z| = Y – Z = 2 …………… (4)

Solving (3) and (4), we get,
 • Y = 7, and X = 5

Therefore, total amount = 24 * $5 + 7 * $4 + 5 * $3 = $163

Hence, the correct answer is Option A.

Answer: A

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-Algebra-e1533292163516.png

Archit3110 · Answer

given ;
x+y+z=36
y-z-2 ; x=2(y+z)
solve for z=5 , y= 7 and x= 24
so total amount ; 24* 5+7*4+3*5 ; 120+28+15 ; 163 
IMO A

ScottTargetTestPrep · Answer

We can create the equations:

X = 2(Y + Z)

and

X + Y + Z = 36

And

Y - Z = 2 or Z - Y = 2

Since the price of brand Y pen is more than that of brand Z, we want the last equation to be Y - Z = 2 (thus eliminating the equation Z - Y = 2).

Since X = 2(Y + Z), we have:

2(Y + Z) + Y + Z = 36

2Y + 2Z + Y + Z = 36

3Y + 3Z = 36

Y + Z = 12

Adding Y + Z = 12 and Y - Z = 2, we have:

2Y = 14

Y = 7

Thus, Z = 5 and X = 2(7 + 5) = 24.

Therefore, the largest possible total amount that three types of pens will be sold for is:

24 x 5 + 7 x 4 + 5 x 3 = 120 + 28 + 15 = 163

Answer: A

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A store sells brand X pens for 5 dollars each, brand Y pens for $4 eac

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