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Difficulty:
65%
(hard)
Question Stats:
65% (03:03) correct
35%
(02:37)
wrong
based on 34
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In a certain online coding course last semester, there were 17,600 students. This semester, the number of female students increased by 10 percent and the number of male students increased by 22 percent. If the difference between the numbers of female and male students remained unchanged, how many students are in the course this semester?
(A) 19,800
(B) 19,980
(C) 20,000
(D) 20,020
(E) 20,200
(A) 19,800
(B) 19,980
(C) 20,000
(D) 20,020
(E) 20,200
01 Mar 2026, 02:10
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x + y = 17600
This year it will be 1.1x + 1.22y
As difference is same we will get - 0.22y = 0.1x
10x = 22y
On solving further we get value of x = 12100 and y = 5500
For total this year we have to find 1.1x + 1.22y = 20020 (D)
This year it will be 1.1x + 1.22y
As difference is same we will get - 0.22y = 0.1x
10x = 22y
On solving further we get value of x = 12100 and y = 5500
For total this year we have to find 1.1x + 1.22y = 20020 (D)
GraemeGmatPanda
Joined: 13 Apr 2020
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02 Mar 2026, 04:49
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We first define variables for the numbers of female and male students last semester
\(F_1 = \text{number of female students last semester}\)
\(M_1 = \text{number of male students last semester}\)
We translate the total number of students last semester
\(F_1 + M_1 = 17,600\)
We translate the 10 percent increase in female students
\(F_2 = 1.1 \times F_1\)
We translate the 22 percent increase in male students
\(M_2 = 1.22 \times M_1\)
We translate the condition that the difference remains the same
\(F_1 - M_1 = F_2 - M_2\)
We substitute for \(F_2\) and \(M_2\) and simplify
\(F_1 - M_1 = 1.1F_1 - 1.22M_1\)
\(-0.1F_1 + 0.22M_1 = 0\)
\(0.22M_1 = 0.1F_1\)
We isolate \(F_1\) in terms of \(M_1\)
\(F_1 = 2.2\times M_1\)
We substitute into the total to form one equation in \(M_1\)
\(2.2M_1 + M_1 = 17,600\)
\(3.2M_1 = 17,600\)
We divide to solve for \(M_1\)
\(M_1 = \frac{17,600}{3.2} = \frac{176,000}{32} = \frac{160,000}{32} + \frac{16,000}{32} = 5,000 + 500 = 5,500\)
We find the number of female students last semester
\(F_1 = 2.2 \times 5,500 = (2 + 0.2) \times 5,500 = 11,000 + 1,100 = 12,100\)
We calculate the new number of female students
\(F_2 = 1.1 \times 12,100 = 12,100 + 1,210 = 13,310\)
We calculate the new number of male students
\(M_2 = 1.22 \times 5,500 = 5,500 + 1,210 = 6,710\)
We sum to find the total this semester
\(\text{Total} = F_2 + M_2 = 13,310 + 6,710 = 20,020\)
Answer D
Hope this helps!
ʕ•ᴥ•ʔ
\(F_1 = \text{number of female students last semester}\)
\(M_1 = \text{number of male students last semester}\)
We translate the total number of students last semester
\(F_1 + M_1 = 17,600\)
We translate the 10 percent increase in female students
\(F_2 = 1.1 \times F_1\)
We translate the 22 percent increase in male students
\(M_2 = 1.22 \times M_1\)
We translate the condition that the difference remains the same
\(F_1 - M_1 = F_2 - M_2\)
We substitute for \(F_2\) and \(M_2\) and simplify
\(F_1 - M_1 = 1.1F_1 - 1.22M_1\)
\(-0.1F_1 + 0.22M_1 = 0\)
\(0.22M_1 = 0.1F_1\)
We isolate \(F_1\) in terms of \(M_1\)
\(F_1 = 2.2\times M_1\)
We substitute into the total to form one equation in \(M_1\)
\(2.2M_1 + M_1 = 17,600\)
\(3.2M_1 = 17,600\)
We divide to solve for \(M_1\)
\(M_1 = \frac{17,600}{3.2} = \frac{176,000}{32} = \frac{160,000}{32} + \frac{16,000}{32} = 5,000 + 500 = 5,500\)
We find the number of female students last semester
\(F_1 = 2.2 \times 5,500 = (2 + 0.2) \times 5,500 = 11,000 + 1,100 = 12,100\)
We calculate the new number of female students
\(F_2 = 1.1 \times 12,100 = 12,100 + 1,210 = 13,310\)
We calculate the new number of male students
\(M_2 = 1.22 \times 5,500 = 5,500 + 1,210 = 6,710\)
We sum to find the total this semester
\(\text{Total} = F_2 + M_2 = 13,310 + 6,710 = 20,020\)
Answer D
Hope this helps!
ʕ•ᴥ•ʔ
