GMAT 自作練習問題集

自分のレベル・弱点に合わせた問題を集めるノート。 「同じパターンを繰り返し練習する」ためのリソース。

使い方

推奨学習法

1. 教材で間違えた問題を、似たパターンの自作問題で演習
2. 重要公式を使う問題を自分で作る → 理解の深化
3. 時間制限付きで解く（実戦感覚）

Quant 練習問題

Algebra

問題 Q-A-001（難度: 中）

If x² - 5x + 6 = 0 and y² - 7y + 12 = 0, what is the sum of all possible values of x + y?

(A) 5 (B) 7 (C) 12 (D) 14 (E) 16

解答: (D) 解説:

• x² - 5x + 6 = 0 → (x-2)(x-3) = 0 → x = 2 or 3
• y² - 7y + 12 = 0 → (y-3)(y-4) = 0 → y = 3 or 4
• 全可能な x + y: 2+3=5, 2+4=6, 3+3=6, 3+4=7
• 合計: 5+6+6+7 = 24（重複を考慮しない場合）
• 重複ありなら 24、重複なしなら 5+6+7 = 18
• もし「distinct values of x+y」なら: 5, 6, 7 → 合計 18
• 正解はパターンによる（要確認）

問題 Q-A-002（難度: 易）

If 3^x = 27, what is the value of x?

(A) 3 (B) 9 (C) 27 (D) 81 (E) 243

解答: (A) 解説: 3^x = 27 = 3³, よって x = 3

Arithmetic / Number Properties

問題 Q-N-001（難度: 中）

What is the smallest positive integer that is divisible by both 12 and 18?

(A) 24 (B) 36 (C) 48 (D) 72 (E) 144

解答: (B) 解説: LCM(12, 18) = 36

• 12 = 2² × 3
• 18 = 2 × 3²
• LCM = 2² × 3² = 36

問題 Q-N-002（難度: 中）

If n is a positive integer and n³ + 2n is divisible by 4, what is the smallest possible value of n?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

解答: (B) 解説:

• n=1: 1+2=3, 4で割り切れない
• n=2: 8+4=12, 12÷4=3, 割り切れる
• n=2 が最小

Geometry

問題 Q-G-001（難度: 中）

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

(A) 10 (B) 12 (C) 14 (D) 16 (E) 24

解答: (A) 解説: 三平方の定理 √(6² + 8²) = √(36+64) = √100 = 10

問題 Q-G-002（難度: 高）

A circle is inscribed in a square with side length 10. What is the area of the region between the square and the circle?

(A) 100 - 25π (B) 100 - 100π (C) 100 - 50π (D) 50 - 25π (E) 50π - 100

解答: (A) 解説:

• 正方形面積: 100
• 内接円の半径: 5（正方形辺長の半分）
• 円面積: π × 5² = 25π
• 差: 100 - 25π

Word Problems

問題 Q-W-001（難度: 中）

A train travels from city A to city B at 60 mph and returns from B to A at 40 mph. What is the average speed for the entire trip?

(A) 48 mph (B) 50 mph (C) 52 mph (D) 55 mph (E) 100 mph

解答: (A) 解説:

• 平均速度 = 総距離 / 総時間（速度の単純平均ではない）
• 距離 d とすると、行き時間 = d/60、帰り時間 = d/40
• 総時間 = d/60 + d/40 = (2d + 3d) / 120 = 5d/120 = d/24
• 総距離 = 2d
• 平均速度 = 2d ÷ d/24 = 2d × 24/d = 48 mph

問題 Q-W-002（難度: 中）

Worker A can complete a job in 6 hours, and Worker B can complete the same job in 4 hours. How long would it take them to complete the job working together?

(A) 1.5 hours (B) 2 hours (C) 2.4 hours (D) 2.5 hours (E) 3 hours

解答: (C) 解説:

• A の仕事率: 1/6
• B の仕事率: 1/4
• 合計: 1/6 + 1/4 = 2/12 + 3/12 = 5/12
• 時間 = 1 ÷ 5/12 = 12/5 = 2.4 時間

Probability / Combinatorics

問題 Q-P-001（難度: 中）

A bag contains 3 red and 5 blue balls. If 2 balls are drawn without replacement, what is the probability that both are red?

(A) 3/28 (B) 3/14 (C) 9/64 (D) 1/4 (E) 1/2

解答: (A) 解説:

• P(1個目赤) = 3/8
• P(2個目赤 | 1個目赤) = 2/7
• P(両方赤) = 3/8 × 2/7 = 6/56 = 3/28

問題 Q-P-002（難度: 中）

A committee of 3 is to be formed from 5 men and 4 women. How many committees include at least 1 woman?

(A) 60 (B) 64 (C) 70 (D) 74 (E) 84

解答: (D) 解説:

• 全組み合わせ: C(9, 3) = 84
• 女性ゼロ（全員男性）: C(5, 3) = 10
• 少なくとも1人女性: 84 - 10 = 74

Verbal 練習問題

CR - Strengthen

問題 V-CR-001（難度: 中）

Studies have shown that employees who take regular breaks during their workday are 25% more productive than those who don't. Therefore, companies should mandate at least two 15-minute breaks for all employees during work hours.

Which of the following, if true, would most strengthen the conclusion above?

(a) Most employees prefer to have flexibility in their schedules. (b) Companies that have implemented mandatory break policies have seen significant increases in overall productivity. (c) Some studies suggest that breaks longer than 15 minutes are even more beneficial. (d) Employee retention rates are higher in companies with relaxed break policies. (e) Many employees already take informal breaks throughout the day.

解答: (b) 解説: (b) は実際の企業がマンダトリーブレイク政策を導入して効果が出たという直接的証拠で、結論「企業はマンダトリー化すべき」を最も強く支持。

CR - Weaken

問題 V-CR-002（難度: 中）

The government plans to reduce traffic congestion by building more roads. Since traffic congestion has been worsening over the past decade, this plan should significantly improve the situation.

Which of the following, if true, would most weaken the argument?

(a) Building roads is expensive and time-consuming. (b) Other cities have failed to reduce congestion through similar measures. (c) Studies show that adding road capacity often induces additional traffic, ultimately offsetting any reduction in congestion. (d) Public transportation is a more sustainable solution than building roads. (e) The government has limited budget for infrastructure projects.

解答: (c) 解説: (c) は「道路を増やしても新たな交通需要を生み出し、最終的に渋滞は改善されない」という直接的反論。"induced demand" の現象に基づく弱体化。

RC

Sample Passage V-RC-001

The notion that economic growth necessarily leads to environmental degradation has been a central tenet of much environmental thinking. Yet some economists, applying the so-called Environmental Kuznets Curve hypothesis, argue that the relationship between economic growth and environmental quality is not linear but inverted U-shaped: as countries develop, environmental degradation initially worsens, but after reaching a certain income threshold, environmental quality begins to improve.

Critics of this hypothesis, however, point to several limitations. First, the curve has been observed primarily for local pollutants such as sulfur dioxide, but not consistently for global pollutants like carbon dioxide. Second, the threshold income level appears to vary considerably by country, suggesting that institutional and policy factors play a critical role. Third, the historical pattern observed in developed countries may not hold for emerging economies in a global trading system, where pollution can be exported through outsourcing.

Q1: Main Idea

The primary purpose of the passage is to: (a) advocate for environmental policy reform (b) describe the Environmental Kuznets Curve hypothesis and discuss its limitations (c) compare developed and emerging economies (d) prove that economic growth causes environmental degradation (e) propose a new economic theory

解答: (b) 解説: パッセージは EKC 仮説の説明と、その限界を論じている。最も包括的な選択肢は (b)。

Q2: Inference

Based on the passage, critics of the Environmental Kuznets Curve hypothesis would most likely agree that: (a) economic growth always harms the environment (b) developing countries should not pursue economic growth (c) global pollutants present challenges that the EKC hypothesis cannot fully address (d) sulfur dioxide is the most important pollutant to consider (e) all developed countries have improved their environmental quality

解答: (c) 解説: パッセージは「the curve has been observed primarily for local pollutants such as sulfur dioxide, but not consistently for global pollutants like carbon dioxide」と述べている。

Data Insights 練習問題

DS

問題 DI-DS-001（難度: 中）

Is x² > 25? (1) x > 5 (2) x is positive

解答: (A) 解説:

• (1) x > 5 → x² > 25（x が正で 5 超ならOK）→ Sufficient
• (2) x > 0 → x² > 25 とは限らない（x = 1 なら x² = 1）→ Not Sufficient
• 答え: A

問題 DI-DS-002（難度: 中）

What is the value of |x - 5|? (1) x = 8 (2) x² = 64

解答: (A) 解説:

• (1) x = 8 → |8-5| = 3 → Sufficient
• (2) x² = 64 → x = 8 or -8
  • x = 8 なら |3| = 3
  • x = -8 なら |-13| = 13
  • 異なる値 → Not Sufficient
• 答え: A

自作問題作成のコツ

良い問題の特徴

• 明確な解法プロセス
• 罠選択肢が論理的に設計されている
• 複数の概念を統合
• 計算量が適度（GMAT は計算機械力テストではない）

自作のステップ

1. 教材で間違えた問題のパターンを抽出
2. 数値・文脈を変えて類題作成
3. 自分で解いて時間計測
4. 友人・チューターにレビュー依頼

練習量の目安

Phase 1（基礎期）

• Quant: 100-200 問
• Verbal: 50-100 問
• DI: 50-100 問

Phase 2（応用期）

• Quant: 300-500 問
• Verbal: 200-300 問
• DI: 100-200 問

Phase 3（仕上げ期）

• Quant: 200 問の解き直し
• Verbal: 100 問の解き直し
• DI: 100 問の解き直し

合計

• 約 1,500-2,000 問が標準
• このうち 500 問は反復演習

問題演習記録テンプレート

## YYYY-MM-DD 演習記録

### セッション情報
- 開始: HH:MM
- 終了: HH:MM
- 時間: ___ 分

### 演習量
- Quant: ___ 問
- Verbal: ___ 問
- DI: ___ 問

### 正答率
- Quant: ___ %
- Verbal: ___ %
- DI: ___ %

### 弱点問題（# 番号 + 理由）
- _____

### 学び
- _____