Basmati rice costs $(a-b) per kilogram in standard 7-

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Basmati rice costs $(a-b) per kilogram in standard 7-

by BTGmoderatorLU » Fri Oct 18, 2019 3:13 am

Source: Economist GMAT

Basmati rice costs $$(a-b)$ per kilogram in standard 7-kilogram packages, where $a > b > 0$ and $$(a)$ per kilogram in non-standard packages. In terms of $a$ and $b$, what is the lowest possible price of exactly 24 kilograms of Basmati rice, in dollars?

A. $24a-3b$
B. $21a-3b$
C. $24a-21b$
D. $21a-21b$
E. $21a-24b$

The OA is C

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Source: Beat The GMAT — Problem Solving | Fri Oct 18, 2019 3:13 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Sat Oct 19, 2019 4:12 pm

1kg of Basmati rice => $( a - b) for standard packages
One standard package = 7kg => $7( a - b)
1kg of basmati rice => $ (a) for non-standard packages
a> b > o => a > o and b > o and a > b
Both a and b are positive integers
Note: standard packages are heavier/greater than non-standard packages
For lowest possible price of exactly 24kg of basmati rice => $$\frac{24kg}{i\ s\tan dard\ \ package}$$
where 1 standard package - 7kg
24kg / 7 kg = 3 remainder 3
Hence, in exactly 24kg, there will be 3 standard package and 3 non-standard package
If the price of 1 standard package = $7 (a - b )
3 standard package = $7 * 3 ( a - b ) = $21 ( a - b )
For non-standard packages;
1 non-standard package = 1kg = $a
3 non-standard package = 3kg = $3a
Total price = price of standard package + price of non-standard package
= [$21 ( a - b ) ] + $3
= $21a - $21b + $3a
= $24a - $21b
Answer= option C

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by Scott@TargetTestPrep » Sun Oct 20, 2019 9:09 am

BTGmoderatorLU wrote:Source: Economist GMAT

Basmati rice costs $$(a-b)$ per kilogram in standard 7-kilogram packages, where $a > b > 0$ and $$(a)$ per kilogram in non-standard packages. In terms of $a$ and $b$, what is the lowest possible price of exactly 24 kilograms of Basmati rice, in dollars?

A. $24a-3b$
B. $21a-3b$
C. $24a-21b$
D. $21a-21b$
E. $21a-24b$

The OA is C

The most economical way to buy 24 kilograms of rice is to buy three 7-kg packages and three 1-kg non-standard packages. Thus, the lowest cost is:

21(a - b) + 3a = 21a - 21b + 3a = 24a - 21b

Answer: C

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