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19 Jan 2026, 05:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
77% (02:00) correct
23%
(01:48)
wrong
based on 100
sessions
History
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Not Attempted Yet
At Bailey’s bike shop, 75 percent of the bikes sold are mountain bikes, and the rest are road bikes. What percentage of the bikes sold are mountain bikes for kids?
(1) Twenty percent of the bikes sold are for kids and 80 percent are for adults.
(2) Twenty percent of the bikes sold are road bikes for adults.
(1) Twenty percent of the bikes sold are for kids and 80 percent are for adults.
(2) Twenty percent of the bikes sold are road bikes for adults.
15 Mar 2026, 01:51
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At Bailey’s bike shop, 75 percent of the bikes sold are mountain bikes, and the rest are road bikes. What percentage of the bikes sold are mountain bikes for kids?
(1) Twenty percent of the bikes sold are for kids and 80 percent are for adults.
(2) Twenty percent of the bikes sold are road bikes for adults.
Let the total number of bikes sold be 'T', out of which 'M' be the number of mountain bikes sold, and 'R' be the number of road bikes sold.
Given: Number of mountain bikes sold = 3/4 T = 0.75 T
Number of road bikes sold = 1/4 T = 0.25 T
We need to find out the percentage of the bikes sold are mountain bikes for kids.
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: Twenty percent of the bikes sold are for kids and 80 percent are for adults.
Number of bikes sold to kids = 0.2 T
Number of bikes sold to adults = 0.8 T
However, we don’t know how those 0.2T bikes split between mountain vs road. Thus, this statement is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Twenty percent of the bikes sold are road bikes for adults.
Number of road bikes for adults = 1/5 T
Hence, the number of road bikes for kids = 1/4 T - 1/5 T = 1/20 T
However, we still don't know how mountain bikes split between kids and adults. Thus, this statement is insufficient alone.
Now, let's look at the combination of both the statements:
Mountain bikes for kids = 1/5 T - 1/20 T = 3/20 T
Thus, the percentage of the bikes sold that are mountain bikes for kids = (3/20 T) / T * 100 = 15%
Hence, the correct answer is Option C - BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Hope this helps!
(1) Twenty percent of the bikes sold are for kids and 80 percent are for adults.
(2) Twenty percent of the bikes sold are road bikes for adults.
Let the total number of bikes sold be 'T', out of which 'M' be the number of mountain bikes sold, and 'R' be the number of road bikes sold.
Given: Number of mountain bikes sold = 3/4 T = 0.75 T
Number of road bikes sold = 1/4 T = 0.25 T
We need to find out the percentage of the bikes sold are mountain bikes for kids.
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: Twenty percent of the bikes sold are for kids and 80 percent are for adults.
Number of bikes sold to kids = 0.2 T
Number of bikes sold to adults = 0.8 T
However, we don’t know how those 0.2T bikes split between mountain vs road. Thus, this statement is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Twenty percent of the bikes sold are road bikes for adults.
Number of road bikes for adults = 1/5 T
Hence, the number of road bikes for kids = 1/4 T - 1/5 T = 1/20 T
However, we still don't know how mountain bikes split between kids and adults. Thus, this statement is insufficient alone.
Now, let's look at the combination of both the statements:
Mountain bikes for kids = 1/5 T - 1/20 T = 3/20 T
Thus, the percentage of the bikes sold that are mountain bikes for kids = (3/20 T) / T * 100 = 15%
Hence, the correct answer is Option C - BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Hope this helps!
15 Mar 2026, 11:10
Kudos
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This is an overlapping sets problem and the key is tracking what we know about each category.
Given: 75% mountain bikes, 25% road bikes
We need: % of all bikes that are kids' mountain bikes
Statement (1) alone: 20% for kids, 80% for adults.
From this, we know 20% of total bikes are for kids. But we don't know what portion of those kids' bikes are mountain vs road. Could be all mountain, could be all road, could be mixed.
So (1) is insufficient.
Statement (2) alone: 20% are road bikes for adults.
Total road bikes = 25%. If 20% are road bikes for adults, then road bikes for kids = 25% - 20% = 5%.
Now, total kids' bikes = unknown (unlike statement 1). So we can't determine kids' mountain bikes.
So (2) is insufficient.
Together: From (1), kids' bikes = 20%. From (2), kids' road bikes = 5%.
Therefore, kids' mountain bikes = 20% - 5% = 15%.
Together they're sufficient.
Answer: C
The trick is recognizing that you need both the total kids percentage and the breakdown by type to solve this. Common setup for DS problems with overlapping categories.
Given: 75% mountain bikes, 25% road bikes
We need: % of all bikes that are kids' mountain bikes
Statement (1) alone: 20% for kids, 80% for adults.
From this, we know 20% of total bikes are for kids. But we don't know what portion of those kids' bikes are mountain vs road. Could be all mountain, could be all road, could be mixed.
So (1) is insufficient.
Statement (2) alone: 20% are road bikes for adults.
Total road bikes = 25%. If 20% are road bikes for adults, then road bikes for kids = 25% - 20% = 5%.
Now, total kids' bikes = unknown (unlike statement 1). So we can't determine kids' mountain bikes.
So (2) is insufficient.
Together: From (1), kids' bikes = 20%. From (2), kids' road bikes = 5%.
Therefore, kids' mountain bikes = 20% - 5% = 15%.
Together they're sufficient.
Answer: C
The trick is recognizing that you need both the total kids percentage and the breakdown by type to solve this. Common setup for DS problems with overlapping categories.
