There are 30 coins in a bag of which 10 are gold. If 25 of the coins

Question

There are 30 coins in a bag of which 10 are gold. If 25 of the coins are rare, then the number of rare gold coins in the bag could be any number from

A) 3 to 5
B) 3 to 10
C) 5 to 10
D) 10 to 15
E) 10 to 25

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rosyln · Answer

IMHO  E is the correct answer. 
Total coins in the bag 30; Gold = 10; Rare = 25
 Minimum rare coins:  If none of the gold coins are rare, then 25 coins must come from the remaining 30 - 10 = 20 non-gold coins. In this case, all 20 non-gold coins are rare, and the remaining 25 - 20 = 5 rare coins must overlap with gold coins. Therefore, the minimum number of rare coins in the bag is 10. 
 Maximum rare coins:   If all 10 gold coins are rare, the rare coins could also include up to 30 - 10 = 20 non-gold coins. However, the problem states there are only 25 rare coins in total. So, the maximum number of rare coins is 25.
 Final range:  The number of rare coins in the bag can range from 10 to 25.

cdrectenwald · Answer

To solve this, let’s analyze the problem step by step:
 1. Total Coins in the Bag: 30 coins.
 2. Gold Coins: 10 coins.
 3. Rare Coins: 25 coins.

We need to determine how many of the gold coins (10) are also rare.

Key Observations:

• Since there are 10 gold coins, the number of rare gold coins cannot exceed 10.
 • There are 25 rare coins in total, so at least ￼ rare coins must be non-gold. This means up to ￼ rare coins could be gold.

Range of Rare Gold Coins:

• The minimum number of rare gold coins could be ￼ (if none of the rare coins are gold).
 • The maximum number is all 10 gold coins (if all are rare).

So, the range is 5 to 10 thus C

BraydinWalters · Answer

When I see a question like this, I like to first setup a table:

Gold 
 Not Gold 
 Total 
 
  Rare

Not Rare

Total

The following information is provided:
 
 We have a total of 30 coins in the bag 
 10 of the coins are gold 
 25 are rare

We can add these to the table and fill-in some additional boxes (highlighted numbers were provided, others calculated:

Gold 
 Not Gold 
 Total 
 
  Rare 
 X 
  
   25   
 
  Not Rare

30 - 25 =  5  
 
  Total 
   10   
 30 - 10 =  20  
   30

Notice the following:
 
 If there are 10 total gold coins and 25 total rare coins, then the maximum  gold AND rare  coins you can have is 10. Eliminate answers D and E.

Lets test a minimum of 3  gold AND rare  coins. 
 
 With 3  gold AND rare  coins and a total of 25 rare coins, that would mean we have 22  not gold AND rare  coins.

Gold 
 Not Gold 
 Total 
 
  Rare 
  3  
  25 - 3 = 22  
 25 
 
  Not Rare

5 
 
  Total 
 10 
  20  
 30

Notice:
 
 We determined that the total coins that are not gold is 20. So there cannot be 22  not gold AND rare  coins. 
 Eliminate Answers A and B.

C

BHARGAVIMOGADALA · Answer

Total Coins in the Bag = 30
Number of Gold Coins = 10
Total Number of Rare Coins = 25

So, 30−25=5 coins are not rare coins.

Let’s find the possible number of rare gold coins:
I. Since the total number of gold coins is 10, the maximum number of rare gold coins can be at most 10.
II. If all the non-rare coins (5) are gold, the minimum number of rare gold coins would be 10-5 = 5.

Therefore, the number of rare gold coins in the bag can range from a min. of 5 to a max. of 10, and the answer is  C (5 to 10).

prantorboni · Answer

There are 30 coins in a bag of which 10 are gold. If 25 of the coins are rare, then the number of rare gold coins in the bag could be any number from

There are 25 rare coins & 10 gold coins. Now, 25+10=35 which means, there are certainly 5 gold coins which are rare. Now, the rest 5 gold coins may be rare or may not be. So, the range would be, 5 to 10.

Answer: C) 5 to 10.

flippedeclipse · Answer

This is easiest to visualize using a table.

Rare 
 Not Rare 
 Total 
 
  Gold 
  Value Needed  
  
 10 
 
  Not Gold

20 
 
  Total 
 25 
 5 
 30

Question asks us to both minimize AND maximize the value of rare gold coins.

Looking across Row 2, we can see that the max number of gold coins possible is 10, assuming there are zero non-rare gold coins. So that's the absolute maximum value.

Looking down Column 2 is the tricky bit. To  minimize  rare gold coins, we need to  maximize  rare, not gold coins. What's the max value for that cell? 20, because if there are zero non-rare, non-gold coins, that means there are 20 non-gold rare coins. Subtracting total rare coins from this maximized value of not-gold coins, we get 5 as the minimum possible value.

Thus, range is 5 to 10, answer C.

There are 30 coins in a bag of which 10 are gold. If 25 of the coins

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	Gold	Not Gold	Total
Rare	X		25
Not Rare			30 - 25 = 5
Total	10	30 - 10 = 20	30

GMAT Problem Solving (PS) Questions

There are 30 coins in a bag of which 10 are gold. If 25 of the coins

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