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Problem Solving Butler: January 2025
January 8PS 1PS 2

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PS 1

What are the last two digits (at tens place and units place) in the numerical value of 49^852 + 11^77 ?

A. 52
B. 60
C. 72
D. 82
E. 92

_____________________________
PS 2

Suppose that x = 1/2 is the only real number that satisfies \(3^{(-2x^2 + 4Ax - \frac{9}{5})}=√27\). What is the value of A?

A. 19/5
B. 19/10
C. 19/20
D. 53/10
E. 53/20
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Data Sufficiency Butler: January 2025
January 9DS 1DS 2

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DS 1

Last year, in Crossia, 25% of all babies were delivered in a private hospital, while 40% of all cesarean births occurred in a private hospital. Last year, in Crossia, what percentage of all births that took place in a private hospital were cesarean births?

(1) Last year, in Crossia, a total of 72,000 babies were delivered in a private hospital.
(2) Last year, in Crossia, 20% of all births were caesareans.
___________________________
DS 2

What is the average (arithmetic mean) mileage of 7 cars in a parking lot?

(1) If the 7 mileages were ordered from least to most, each would be 2.5 miles per gallon higher than the preceding car’s mileage.
(2) The range of the 7 mileages is 15 miles per gallon.
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Critical Reasoning Butler: January 2025
January 9CR 1CR 2

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CR 1

Due to certain persistent limitations in the technology, many early buyers of virtual reality systems apparently lost interest in buying new virtual reality games to run on their systems. The sale of virtual reality games is still going strong because the number of homes with virtual reality systems is still growing. However, businesses distributing virtual reality games will face hard times because the market for virtual reality systems is likely to saturate soon.

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

A. The market for virtual reality systems is considered saturated only after seventy percent of all homes have at least one such system.
B. Early buyers of novel products are always quicker to acquire novelties, but also quicker to tire of them than other buyers.
C. Customer satisfaction surveys reveal that few of the early buyers of virtual reality systems had any complaints regarding this new product’s performance aspects.
D. Several games specifically designed to be played in virtual reality form a sizeable proportion of all the products handled by retailers of virtual reality games.
E. Shrinking markets generally intensify competition among businesses, leading to the failure of several marginal businesses.
___________________________
CR 2

At the time of the last census, the number of military veterans was slightly greater than the number of conservatives. Military veterans have tripled in number since then, while conservatives have increased in number, but at a lower rate than have military veterans.

Which of the following must be true if the statements above are true?

A. There are now fewer military veterans than there are conservatives.
B. The ratio between military veterans and conservatives has increased since the last census.
C. The ratio between military veterans and conservatives has decreased since the last census.
D. Every conservative is also a military veteran.
E. The ratio between military veterans and conservatives has not changed since the last census.
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Problem Solving Butler: January 2025
January 9PS 1PS 2

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PS 1

If N is a positive integer and N! is divisible by 143, what is the lowest possible value of N ?

A. 10
B. 11
C. 13
D. 142
E. 143
________________________
PS 2

If n is a positive integer and n^2 is divisible by 120, which is the highest positive integer that must divide n ?

A. 24
B. 30
C. 60
D. 90
E. 120
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Hi everyone 👋
I’m confused about this geometry question. It only gives AB = BE, AB ∥ CD, and AE ∥ FC, but the solution seems to assume AD ∥ BC (outer figure is a rectangle/parallelogram), which isn’t stated.
Without AD ∥ BC, the angle at F isn’t fixed.
Am I missing something here?
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RobinMitra

Hi everyone 👋
I’m confused about this geometry question. It only gives AB = BE, AB ∥ CD, and AE ∥ FC, but the solution seems to assume AD ∥ BC (outer figure is a rectangle/parallelogram), which isn’t stated.
Without AD ∥ BC, the angle at F isn’t fixed.
Am I missing something here?

Geometry questions like this are no longer part of the GMAT syllabus, so you can safely ignore it and move on.
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