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A
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Difficulty:
55%
(hard)
Question Stats:
57% (02:38) correct
43%
(02:49)
wrong
based on 21
sessions
History
Date
Time
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Not Attempted Yet
At an economic summit, the only attendees are 18 finance ministers, their spouses, their assistants, and 24 journalists. Each finance minister brought either 2 or 3 assistants. Exactly y ministers attended without their spouses. If there are x attendees in all, how many finance ministers brought three assistants, in terms of x and y?
A. x - 96 + y
B. x - 96 - y
C. x - 78 + y
D. x - 78 - y
E. x - 60 + y
A. x - 96 + y
B. x - 96 - y
C. x - 78 + y
D. x - 78 - y
E. x - 60 + y
12 Mar 2026, 02:58
Kudos
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The key concept here is setting up a counting equation and isolating the unknown variable — this is a classic Word Problem / Algebraic Expression question on the GMAT Focus.
The common trap: students try to solve for the number of ministers who brought 3 assistants directly without first building the total-count equation. Instead, work backwards from x.
Let k = number of finance ministers who brought 3 assistants (this is what we want).
Then (18 − k) ministers brought 2 assistants.
Step 1 — Count every group at the summit:
• Finance ministers: 18
• Spouses: y ministers came WITHOUT a spouse, so (18 − y) brought a spouse → (18 − y) spouses
• Assistants: k ministers brought 3 each, and (18 − k) brought 2 each → 3k + 2(18 − k) = 3k + 36 − 2k = k + 36
• Journalists: 24
Step 2 — Write the total equation:
x = 18 + (18 − y) + (k + 36) + 24
x = 18 + 18 − y + k + 36 + 24
x = 96 − y + k
Step 3 — Solve for k:
k = x − 96 + y
The answer is A.
Common trap: Some students forget that the y ministers who came WITHOUT a spouse still count as ministers — so the minister count stays 18, but the spouse count drops by y. Keep those two groups separate in your accounting.
Takeaway: In "how many in terms of x and y" problems, always build your total expression first, then isolate the target variable by moving everything else to the other side.
The common trap: students try to solve for the number of ministers who brought 3 assistants directly without first building the total-count equation. Instead, work backwards from x.
Let k = number of finance ministers who brought 3 assistants (this is what we want).
Then (18 − k) ministers brought 2 assistants.
Step 1 — Count every group at the summit:
• Finance ministers: 18
• Spouses: y ministers came WITHOUT a spouse, so (18 − y) brought a spouse → (18 − y) spouses
• Assistants: k ministers brought 3 each, and (18 − k) brought 2 each → 3k + 2(18 − k) = 3k + 36 − 2k = k + 36
• Journalists: 24
Step 2 — Write the total equation:
x = 18 + (18 − y) + (k + 36) + 24
x = 18 + 18 − y + k + 36 + 24
x = 96 − y + k
Step 3 — Solve for k:
k = x − 96 + y
The answer is A.
Common trap: Some students forget that the y ministers who came WITHOUT a spouse still count as ministers — so the minister count stays 18, but the spouse count drops by y. Keep those two groups separate in your accounting.
Takeaway: In "how many in terms of x and y" problems, always build your total expression first, then isolate the target variable by moving everything else to the other side.
12 Mar 2026, 06:41
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kevincan
Let the finance ministers be 18.
Let the finance minister without spouse be y.
Let the finance minister with spouse = (18-y).
Journalist = 24
Let the number of 2 assistants be a.
Let the number of 3 assistants be (18-a).
Total = x
X = Finance Minister + FM (with spouse) + Journalist + 2*a +3 * (18-a)
x = 18 + (18-y) + 24 + 2a +3*(18-a)
x = 116 - y - a
x - 116 +y = -a
We need to find : (18-a)
Adding 18 on both sides , we get
18 + x - 116 + y = 18 - a
x - 96 + y = (18-a)
Option A
