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Probability is one of the most important GMAT Quant topics because it often combines logic, counting, set theory, and permutations & combinations. Many students try to solve probability questions by listing every possible case, but GMAT probability...- Jun 10
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04 May 2026, 20:25
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| Problem Solving Butler: May 2025 | ||
| May 5 | PS 1 | PS 2 |
______________________
PS 1
If x is positive, which of the following may be the correct ordering of \(\frac{1}{x}\), \(x\), \(x^2\), \(x^3\) ?
I. \(\frac{1}{x} < x < x^2 < x^3\)
II. \(\frac{1}{x} < x^3 < x^2 < x\)
III. \(x^3 < x^2 < x < \frac{1}{x}\)
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
______________________
PS 2
If |x| > 5 – 2x, which of the following represents the correct range of values of x ?
A. x > 5/3
B. x > 5
C. 5/3 < x < 5
D. -5 < x < -5/3
E. No such real value of x exists
04 May 2026, 20:28
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| Critical Reasoning Butler: May 2025 | ||
| May 5 | CR 1 | CR 2 |
________________________
CR 1
Over the last fifteen years, the consumption of beef has decreased significantly in many parts of the world. This decrease has coincided with an increasing public awareness of the adverse environmental effects of cattle ranching. Thus, the decrease in beef consumption must have been caused by the consumers’ awareness of the environmentally damaging effects of cattle ranching.
Which of the following, if true, most seriously calls into question the explanation above?
A. On average, people consume twenty percent less beef today than they did fifteen years ago.
B. Habitual beef eaters may suffer mild gastrointestinal distress for a few weeks or so after significantly reducing their beef consumption.
C. Beef prices increased steadily in the last fifteen years because of the degradation of land used to graze cattle.
D. The consumption of poultry, fish, and other forms of seafood has increased over the last fifteen years.
E. Gourmet beef sales have held steady as sales of regular beef have declined.
________________________
CR 2
A promising student of taekwondo once asked his coach how long it would take him to earn his black belt, signifying the end of his training. Thinking carefully, the coach replied, “If you practice three hours a day for six days a week, you could earn your black belt in five years.” Unhappy, the student asked, “What if I practice eight hours a day, every day?” The coach then said, “If you do so, you will probably never move beyond a blue belt.”
The main point that the coach makes here is that in martial arts, a critical value is
A. curiosity
B. patience
C. dedication
D. vigor
E. resolution
04 May 2026, 20:34
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| Problem Solving Butler: May 2025 | ||
| May 5 | PS 1 | PS 2 |
_____________________
PS 1
At two specialty food stalls, Green Market and Riverside Market, the prices per kilogram of almonds, walnuts, and pecans were as follows:
| Green Market | Riverside Market | |
| Almonds | $14 | $16 |
| Walnuts | $16 | $18 |
| Pecans | $18 | $20 |
Marcus bought certain quantities of almonds, walnuts, and pecans at Riverside Market. How much money would he have saved if he had bought those same quantities at Green Market instead?
(1) The total weight of nuts Marcus bought was 4.5 kilograms.
(2) For every 2 kilograms of walnuts Marcus bought, he bought 3 kilograms of pecans and 5 kilograms of almonds.
_____________________
PS 2
At a certain car dealership, what percent of the cars both weigh more than 1,800 kilograms and cost more than €40,000?
(1) 55% of all the cars at the dealership weigh more than 1,800 kilograms.
(2) Of the cars at the dealership that weigh more than 1,800 kilograms, 20% cost more than €40,000.
