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505-555 (Easy)|   Word Problems|                     
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carcass
Items that are purchased together at a certain discount store are priced at $3 for the first item purchased and $1 for each additional item purchased. What is the maximum number of items that could be purchased together for a total price that is less than $30 ?

A. 25

B. 26

C. 27

D. 28

E. 29


key here is "total price that is less than $30"
so, the closest price that is less than 30 is $29

$29 - $3 (first item) leaves us with $26
Since all items after the first is equal to $1, then the number of items other than the first is 26 = $26
26 + 1(first item purchased for 3) = 27

therefore the answer is (c) 27
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less than 30 means 29,
so 29 = 3 + (x-1)(1)
26 = x -1
x = 27.
answer C.
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less than 30 means 29,
so 29 = 3 + (x-1)(1)
26 = x -1
x = 27.
answer C.
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Why aren't we using the formula
Sn= n/2(2a + (n-1)×d)
Sn here is the sum of n terms
Here Sn =30
n we need to find
a=3
d=1

Posted from my mobile device
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Items that are purchased together at a certain discount store are priced at $3 for the first item purchased and $1 for each additional item purchased. What is the maximum number of items that could be purchased together for a total price that is less than $30 ?

first item = $3
We're left with $26 to spend on 26 additional items.
additional items = 26

26 + 1 = 27

Answer is C.
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less than 30 dollars = 29$

of the 29$ we have already spent 3$ on the first purchase. so now we're left with 26 $ to spend.

after the first purchase, all the additional purchase is at 1$ each

so, now we have the following equation:
\(3$ + N items (at 1 $ each) = $29\)
N item(at 1 $ each)= 29-3=26
so total items bought = 26+1 = 27 (which is N items bought at 1$ each + the first purchase of 3$)
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carcass
Items that are purchased together at a certain discount store are priced at $3 for the first item purchased and $1 for each additional item purchased. What is the maximum number of items that could be purchased together for a total price that is less than $30 ?

A. 25

B. 26

C. 27

D. 28

E. 29
Solution:

Let x be the number of additional items that can be bought for $29, the maximum whole number of dollars less than $30. We can create the equation:

3 + x = 29

x = 26

We see that we can buy 26 additional items, and including the first item, we can buy 27 items in total.

Answer: C
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Items that are purchased together at a certain discount store are priced at $3 for the first item purchased and $1 for each additional item purchased. What is the maximum number of items that could be purchased together for a total price that is less than $30 ?

It’s given that total price is less than 30$, so the maximum possible price is 29 $
First item cost is 3$ and each additional item cost 1 $.
After purchasing first item for 3 $, we have 26 $ left and with this 26 $ we can purchase 26 additional items.
So, the maximum no of items that could be purchased = 1+ 26 = 27 items

Option C is the answer.

Thanks,
Clifin J Francis
GMAT SME
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Maximum price = $29

1st item = $3 ---> remaining balance = 26, which can be used to buy 26 additional items.

Therefore total no. of items = 1+26 = 27
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Let's break down the pricing to understand the pattern:

- The first item costs $3.
- Each additional item costs $1.

This means that for every additional item purchased, you're only paying $1 more. The goal is to purchase as many items as possible while staying within a total price of less than $30.

Let's calculate:

- For $3, you can purchase 1 item.
- For an additional $1 ($3 + $1 = $4), you can purchase 1 more item.
- For an additional $1 ($4 + $1 = $5), you can purchase 1 more item.
- And so on...

In general, you can purchase n items for a total cost of:
Cost = 3 + (n - 1) x 1 = 2 + n

To keep the total cost under $30:
2 + n < 30

Solving for n:
n < 30 - 2
n < 28

So, the maximum number of items that could be purchased together for a total price less than $30 is 27 items. (n = 27)
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29=3+1x ( x is the number of additional items bought)
29-3=x
26=x

x+1= 27 items
(1 added for the first 3$ item bought)
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