If 3 /7 of the students in a room are seniors and 7/25 of the other students are juniors, and there are x students in the room who are not juniors or seniors, how many students are in the room?
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students in a room:
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Hi manpreet,
This is a legitimate GMAT-style question, but you're going to have to include the answer choices for comparison purposes. They are all likely to be fractions and include the variable (x).
To solve this question, you can TEST a number for the TOTAL NUMBER of students in the room. [spoiler]Try TESTing 175 for the total, solve for the three options (seniors, juniors and other) and you'll have the value of x, which you'll be able to use against the answer choices.[/spoiler]
GMAT assassins aren't born, they're made,
Rich
This is a legitimate GMAT-style question, but you're going to have to include the answer choices for comparison purposes. They are all likely to be fractions and include the variable (x).
To solve this question, you can TEST a number for the TOTAL NUMBER of students in the room. [spoiler]Try TESTing 175 for the total, solve for the three options (seniors, juniors and other) and you'll have the value of x, which you'll be able to use against the answer choices.[/spoiler]
GMAT assassins aren't born, they're made,
Rich
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Brent@GMATPrepNow
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Although manpreet hasn't included the necessary answer choices, I think this is a question type known as "Variables in the Answer Choices," where each answer choice is a variable expression written in terms of x.'manpreet singh wrote:If 3/7 of the students in a room are seniors and 7/25 of the remaining students are juniors, and there are x students in the room who are neither juniors nor seniors, how many students are in the room?
Let's solve it.
Let T = Total number of students in room
So, T = (# of seniors) + (# of juniors) + (others)
3/7 of the students in a room are seniors
So, the # of seniors = (3/7)T
IMPORTANT: We've already accounted for 3/7 of the students. So, 4/7 of the students are not yet accounted for. So, the number of remaining (unaccounted for) students = (4/7)T
7/25 of the remaining students are juniors
So, # of juniors = (7/25)(4/7)T
= (4/25)T
There are x students in the room who are neither juniors nor seniors
So, # of others = x
We're now ready . . .
T = (# of seniors) + (# of juniors) + (others)
T = (3/7)T + (4/25)T + x
Get common denominator: T = (75/175)T + (28/175)T + x
Simplify: T = (103/175)T + x
Subtract (103/175)T from both sides to get: (72/175)T = x
Multiply both sides by (175/72) to get: T = [spoiler](175/72)x[/spoiler]
Aside: If the question were worded, "Which of the following is a possible value of x?," we'd need to recognize that x must be divisible by 72.
Cheers,
Brent
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As Brett mentions above, the answer choices would probably be in terms of x.'manpreet singh wrote:If 3/7 of the students in a room are seniors and 7/25 of the other students are juniors, and there are x students in the room who are not juniors or seniors, how many students are in the room?
An alternate approach would be to plug in a value for the total number of students.
Let the total = the LCM of 7 and 25 = 7*25 = 175.
Seniors = (3/7) * 175 = 75.
Remaining students = 175-75 = 100.
Juniors = (7/25) * 100 = 28.
x = remaining students = 100-28 = 72.
Since the question stem asks for the total number of students, our target is 175.
Now we plug x=72 into the answer choices to see which yields our target of 175.
Answer choice: [spoiler](172/75)x[/spoiler]
(175/72)x = (175/72) * 72 = 175.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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Brent@GMATPrepNow
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Good one, MittGMATGuruNY wrote:As Brett mentions above, the answer choices would probably be in terms of x.'manpreet singh wrote:If 3/7 of the students in a room are seniors and 7/25 of the other students are juniors, and there are x students in the room who are not juniors or seniors, how many students are in the room?
An alternate approach would be to plug in a value for the total number of students.
Let the total = the LCM of 7 and 25 = 7*25 = 175.
Seniors = (3/7) * 175 = 75.
Remaining students = 175-75 = 100.
Juniors = (7/25) * 100 = 28.
x = remaining students = 100-28 = 72.
Since the question stem asks for the total number of students, our target is 175.
Now we plug x=72 into the answer choices to see which yields our target of 175.
Answer choice: [spoiler](172/75)x[/spoiler]
(175/72)x = (175/72) * 72 = 175.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
