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18 Mar 2026, 15:13
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:48) correct
33%
(03:22)
wrong
based on 46
sessions
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Last year, the numbers of oak, elm, and birch trees in Independence Park were in the ratio 2:3:2. Since then, 15 oak trees have been removed, 90 elm trees have been planted, and the number of birch trees has remained unchanged.
If elm trees now account for 3/4 of the total number of trees in the park, how many trees are currently in the park?
A. 180
B. 195
C. 210
D. 225
E. 240
If elm trees now account for 3/4 of the total number of trees in the park, how many trees are currently in the park?
A. 180
B. 195
C. 210
D. 225
E. 240
GraemeGmatPanda
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18 Mar 2026, 16:05
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\(\text{We define }k\text{ as the common multiplier for last year's ratio "2:3:2".}\)
\(o = 2k\)
\(e = 3k\)
\(b = 2k\)
\(\text{From "15 oak trees have been removed" we translate oak now to }2k - 15\text{.}\)
\(o_{\text{now}} = 2k - 15\)
\(\text{From "90 elm trees have been planted" we translate elm now to }3k + 90\text{.}\)
\(e_{\text{now}} = 3k + 90\)
\(\text{Birch is unchanged, so }b_{\text{now}} = 2k\text{. The current total }T\text{ is the sum of the three current counts.}\)
\(T = (2k - 15) + (3k + 90) + 2k\)
\(\text{From "elm trees now account for 3/4 of the total" we write the fraction condition for elm.}\)
\(\frac{3k + 90}{T} = \frac{3}{4}\)
\(\text{Substitute }T\text{ and solve the resulting linear equation for }k\text{.}\)
\(\frac{3k + 90}{(2k - 15) + (3k + 90) + 2k} = \frac{3}{4}\)
\(\frac{3k + 90}{7k + 75} = \frac{3}{4}\)
\(4(3k + 90) = 3(7k + 75)\)
\(12k + 360 = 21k + 225\)
\(360 - 225 = 21k - 12k\)
\(135 = 9k\)
\(k = 15\)
\(\text{Compute the current total }T\text{ using }k = 15\text{.}\)
\(T = 7k + 75\)
\(= 7 \times 15 + 75\)
\(= 105 + 75\)
\(= 180\)
Answer A
Hope this helps!
ʕ•ᴥ•ʔ
\(o = 2k\)
\(e = 3k\)
\(b = 2k\)
\(\text{From "15 oak trees have been removed" we translate oak now to }2k - 15\text{.}\)
\(o_{\text{now}} = 2k - 15\)
\(\text{From "90 elm trees have been planted" we translate elm now to }3k + 90\text{.}\)
\(e_{\text{now}} = 3k + 90\)
\(\text{Birch is unchanged, so }b_{\text{now}} = 2k\text{. The current total }T\text{ is the sum of the three current counts.}\)
\(T = (2k - 15) + (3k + 90) + 2k\)
\(\text{From "elm trees now account for 3/4 of the total" we write the fraction condition for elm.}\)
\(\frac{3k + 90}{T} = \frac{3}{4}\)
\(\text{Substitute }T\text{ and solve the resulting linear equation for }k\text{.}\)
\(\frac{3k + 90}{(2k - 15) + (3k + 90) + 2k} = \frac{3}{4}\)
\(\frac{3k + 90}{7k + 75} = \frac{3}{4}\)
\(4(3k + 90) = 3(7k + 75)\)
\(12k + 360 = 21k + 225\)
\(360 - 225 = 21k - 12k\)
\(135 = 9k\)
\(k = 15\)
\(\text{Compute the current total }T\text{ using }k = 15\text{.}\)
\(T = 7k + 75\)
\(= 7 \times 15 + 75\)
\(= 105 + 75\)
\(= 180\)
Answer A
Hope this helps!
ʕ•ᴥ•ʔ
19 Mar 2026, 18:47
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Let's break this down step by step.
Step 1: Set up the original numbers using the ratio.
The ratio of oak : elm : birch was 2 : 3 : 2. So let's say:
- Oak = 2x
- Elm = 3x
- Birch = 2x
Step 2: Apply the changes.
After the changes:
- Oak = 2x - 15 (15 removed)
- Elm = 3x + 90 (90 planted)
- Birch = 2x (unchanged)
Step 3: Write the new total.
New total = (2x - 15) + (3x + 90) + 2x = 7x + 75
Step 4: Use the condition that elm trees are now 3/4 of the total.
3x + 90 = (3/4)(7x + 75)
Multiply both sides by 4 to clear the fraction:
12x + 360 = 3(7x + 75)
12x + 360 = 21x + 225
360 - 225 = 21x - 12x
135 = 9x
x = 15
Step 5: Find the current total.
Total = 7(15) + 75 = 105 + 75 = 180
Answer: A (180)
The most common mistake here is forgetting to subtract the 15 oaks from the total, which would give you a wrong total formula and a wrong value of x. Note that you should always track every change carefully before setting up your equation.
Step 1: Set up the original numbers using the ratio.
The ratio of oak : elm : birch was 2 : 3 : 2. So let's say:
- Oak = 2x
- Elm = 3x
- Birch = 2x
Step 2: Apply the changes.
After the changes:
- Oak = 2x - 15 (15 removed)
- Elm = 3x + 90 (90 planted)
- Birch = 2x (unchanged)
Step 3: Write the new total.
New total = (2x - 15) + (3x + 90) + 2x = 7x + 75
Step 4: Use the condition that elm trees are now 3/4 of the total.
3x + 90 = (3/4)(7x + 75)
Multiply both sides by 4 to clear the fraction:
12x + 360 = 3(7x + 75)
12x + 360 = 21x + 225
360 - 225 = 21x - 12x
135 = 9x
x = 15
Step 5: Find the current total.
Total = 7(15) + 75 = 105 + 75 = 180
Answer: A (180)
The most common mistake here is forgetting to subtract the 15 oaks from the total, which would give you a wrong total formula and a wrong value of x. Note that you should always track every change carefully before setting up your equation.
