For each order, a certain company charges a delivery fee d : GMAT Data Sufficiency (DS)
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# For each order, a certain company charges a delivery fee d

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For each order, a certain company charges a delivery fee d [#permalink]

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09 Dec 2012, 23:33
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For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and

d = 3, if 0<x<=100
d = 3 + (x-100)/100, if 100<x<=500
d = 7, if x>500

If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than $499? (1) The delivery fee for one of the two orders was$3.
(2) The sum of the delivery fees for the two orders was $10. Need help to tackle such questions under 1.5 mins. source: Gmat Prep [Reveal] Spoiler: OA _________________ Last edited by Bunuel on 10 Dec 2012, 00:15, edited 1 time in total. Renamed the topic and edited the question. Moderator Joined: 02 Jul 2012 Posts: 1231 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Followers: 116 Kudos [?]: 1392 [0], given: 116 Re: For each order [#permalink] ### Show Tags 10 Dec 2012, 00:01 1) Obviously insufficient. The other order could have any value. 2) We can easily create a situation for which the value is more than$499. So lets try to create a situation for which the value is lesser than $499 to prove insufficiency. We can see that atleast one package has to be more than$100. To minimize the value of this , the first package has to be worth $100. So, for insufficiency, the second package can be at most only$399 and so "d" can only be a maximum of nearly $6. But in such a case, the toatl will not add up to 10. Hence the second package HAS to be more than$399.
Sufficient
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Re: For each order [#permalink]

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10 Dec 2012, 00:11
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For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and

d = 3, if 0<x<=100
d = 3 + (x-100)/100, if 100<x<=500
d = 7, if x>500

If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than $499? Notice that the highest charge for the delivery with the second formula is for x=500, thus it equals to d=3+(500-100)/100=$7.

(1) The delivery fee for one of the orders was $3. The price of the merchandise for that order is less than or equal to 100, but we know nothing about the second order. Not sufficient. (2) The sum of the delivery fees for the two orders was$10. If the delivery charges for the two orders are $3 and$7, then the price of the second merchandise must be more than or equal to $500, which means that the total price must be greater than$499. Sufficient.

Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$.

Sufficient

Notice that we can have a case when charges for both deliveries are calculated with the second formula, for example x1=$250 and x2=$350, in this case the total price still would be $10. _________________ Director Joined: 29 Nov 2012 Posts: 898 Followers: 14 Kudos [?]: 1047 [0], given: 543 Re: For each order [#permalink] ### Show Tags 18 Jan 2013, 02:51 Bunuel wrote: For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and d = 3, if 0<x<=100 d = 3 + (x-100)/100, if 100<x<=500 d = 7, if x>500 If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than$499?

Notice that the highest charge for the delivery with the second formula is for x=500, thus it equals to d=3+(500-100)/100=$7. (1) The delivery fee for one of the orders was$3. The price of the merchandise for that order is less than or equal to 100, but we know nothing about the second order. Not sufficient.

(2) The sum of the delivery fees for the two orders was $10. If the delivery charges for the two orders are$3 and $7, then the price of the second merchandise must be more than or equal to$500, which means that the total price must be greater than $499. Sufficient. Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$. So, we have that in both possible cases the total price of the merchandise in the two orders is greater than$499. Sufficient.

Hope it's clear.

Thanks this was really helpful, I missed out on the second case. where there can be 2 values within the range of d=3
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Re: For each order [#permalink]

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26 Mar 2013, 05:36
Bunuel wrote:
For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and

d = 3, if 0<x<=100
d = 3 + (x-100)/100, if 100<x<=500
d = 7, if x>500

If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than $499? Notice that the highest charge for the delivery with the second formula is for x=500, thus it equals to d=3+(500-100)/100=$7.

(1) The delivery fee for one of the orders was $3. The price of the merchandise for that order is less than or equal to 100, but we know nothing about the second order. Not sufficient. (2) The sum of the delivery fees for the two orders was$10. If the delivery charges for the two orders are $3 and$7, then the price of the second merchandise must be more than or equal to $500, which means that the total price must be greater than$499. Sufficient.

Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$.

So, we have that in both possible cases the total price of the merchandise in the two orders is greater than $499. Sufficient. Answer: B. Hope it's clear. Thanks Its really so helpful.I was confused of the statement 2.Now its clear Manager Joined: 12 Dec 2012 Posts: 230 Concentration: Leadership, Marketing GMAT 1: 540 Q36 V28 GMAT 2: 550 Q39 V27 GMAT 3: 620 Q42 V33 GPA: 2.82 WE: Human Resources (Health Care) Followers: 4 Kudos [?]: 78 [0], given: 181 Re: For each order [#permalink] ### Show Tags 14 May 2013, 10:17 Bunuel wrote: [b]Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$ can you please clarify this part more? thanks in advance _________________ My RC Recipe http://gmatclub.com/forum/the-rc-recipe-149577.html My Problem Takeaway Template http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html Manager Joined: 24 Apr 2013 Posts: 54 Schools: Duke '16 Followers: 0 Kudos [?]: 10 [0], given: 76 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags 14 May 2013, 14:55 WOW! I didnt even know where to start i was off and in the end i took a guess and went for B Director Joined: 29 Nov 2012 Posts: 898 Followers: 14 Kudos [?]: 1047 [0], given: 543 Re: For each order [#permalink] ### Show Tags 30 Jul 2013, 04:25 TheNona wrote: Bunuel wrote: [b]Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$ can you please clarify this part more? thanks in advance Cross multiply you will get 300 + x1 - 100 + 300 + x2 - 100 = 1000 After we solve its 600... _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html Manager Joined: 12 Jan 2013 Posts: 244 Followers: 4 Kudos [?]: 69 [0], given: 47 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags 12 Jan 2014, 05:12 Marcab wrote: For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and d = 3, if 0<x<=100 d = 3 + (x-100)/100, if 100<x<=500 d = 7, if x>500 If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than$499?

(1) The delivery fee for one of the two orders was $3. (2) The sum of the delivery fees for the two orders was$10.

Right off the bat, you need to know if: 2*x > 499

1) This one tells you that one of the orders is >= 100, it's insufficient because the other order could be any value

2) This tells you that the total delivery was > 500 + (another value between 1 and 100, inclusive), because there are no other combinations of 3 and 7 other than 3 + 7 that yield 10. So this is clearly sufficient.

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Re: For each order, a certain company charges a delivery fee d [#permalink]

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01 Dec 2015, 12:11
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Re: For each order, a certain company charges a delivery fee d   [#permalink] 01 Dec 2015, 12:11
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