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I’m getting x=-1, how is it x=9?
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4^(4^4) = 2^(2.4^4) = 2^(2*2^8) = 2^(2^9). Equating it with 2^2^x, we get x = 9
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Discussed here: if-x-is-a-real-number-and-4-4-4-2-2-x-what-is-426425.html

If x is a real number and \(4^{(4^{4})} = 2^{(2^x)}\), what is the value of x ?

A. 7
B. 8
C. 9
D. 16
E. 256


\(4^{(4^{4})} = 2^{(2^x)}\)

\((2^2)^{((2^2)^{4})} = 2^{(2^x)}\)

\((2^2)^{(2^8)} = 2^{(2^x)}\)

\(2^{2*2^8} = 2^{(2^x)}\)

\(2^{2^9} = 2^{(2^x)}\)

\( x = 9\)

Answer: C.
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Problem Solving Butler: September 2025
September 25PS 1PS 2

______________________________________
PS 1

A trader used to make 5% profit on an item by selling it at the usual marked price. One day, he tripled the marked price of the item and finally offered a discount of 30%. What is the percentage profit he made on the item that day?

(A) 120.5%
(B) 100%
(C) 94.5%
(D) 90%
(E) 85%
______________________________________
PS 2

A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examination?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Critical Reasoning Butler: September 2025
September 25CR 1CR 2

_____________________________________
CR 1

It is extremely unlikely that the incumbent governor will be voted back to office in the coming elections. According to a recent survey of residents of the state, more than 80% expressed dissatisfaction with the governor’s performance and almost 60% stated that they would vote for the governor’s opponent.

Which of the following most strongly supports the argument?

(A) The views of most of the state’s residents are in concordance with the views of the survey’s respondents.

(B) The governor has received a lot of bad publicity in the past owing to his involvement in a corruption scandal.

(C) The survey only covered a small fraction of the state’s populace.

(D) The governor’s opponent is very popular amongst the residents of the state.

(E) The newspapers in the state are against the governor and favor his opponent instead.
_____________________________________
CR 2

A tricktykart is similar to a bicycle in that a rider uses pedals to propel it ahead. However, since it has three wheels and not two, a tricktykart cannot technically be considered a bicycle and thus tricktykart manufacturers cannot avail of the tax exemptions available to bicycle manufacturers.

Which of the following is assumed in the argument?

(A) Since a tricktykart is very difficult to topple over, it is particularly useful for handicapped people and for those lacking a sense of balance.

(B) Given the similarities between it and a bicycle, a tricktykart should, in fact, be considered a bicycle.

(C) Any self-propelled vehicle that has more than two wheels cannot be considered a bicycle.

(D) The government should make an exemption in the case of a tricktykart, given its importance for handicapped people, and provide tricktykart manufacturers with tax concessions.

(E) A tricktykart cannot run on two wheels.
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Data Sufficiency Butler: September 2025
September 25DS 1DS 2

____________________________________
DS 1

At a used item shop, all caps were priced equally and all sunglasses were priced equally. What was the price of 4 caps and 5 sunglasses at the sale?

(1) The price of a cap was $2.00 more than the price of a sunglasses.
(2) The price of 8 caps and 10 sunglasses was $45.
____________________________________
DS 2

Is the time required to travel d miles at r miles per hour greater than the time required to travel D miles at R miles per hour?

(1) d = D + 20
(2) r = R + 20
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Quote:

*Bunuel writes:*
Data Sufficiency Butler: September 2025

September 25
at-a-used-item-shop-all-caps-were-priced-equally-and-all-sunglasses-450189.html
is-the-time-required-to-travel-d-miles-at-r-miles-per-hour-greater-450190.html



____________________________________
at-a-used-item-shop-all-caps-were-priced-equally-and-all-sunglasses-450189.html

At a used item shop, all caps were priced equally and all sunglasses were priced equally. What was the price of 4 caps and 5 sunglasses at the sale?

(1) The price of a cap was $2.00 more than the price of a sunglasses.
(2) The price of 8 caps and 10 sunglasses was $45.
____________________________________
is-the-time-required-to-travel-d-miles-at-r-miles-per-hour-greater-450190.html

Is the time required to travel d miles at r miles per hour greater than the time required to travel D miles at R miles per hour?

(1) d = D + 20
(2) r = R + 20
DS 2.... I think it’s E....

Question is d/r > D/R ?
Both statements individually are insufficient...
When combined...

d/r = D + 20/R+20...
Now there is also an aspect of relative value of d and r...

Case 1.
d = 1 r = 1...
D becomes 21, R becomes 21

So d/r = D/R
Is d/r > D/R ? No...

Now
d = 10
r = 2
D becomes 30
R becomes 22
d/r > D/R ? Yes... we don’t need to calculate the values ... if d/r is less than 1... then adding 20 each will increase the value...
And if it’s more than 1 then adding 20 each will decrease the value....

Do whether d/r is greater than D/R or no depends on the relative value of d and r... whether d is greater than r or not....

Nice question...
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Here’s the full list of ALL 33 NEW Tables questions we’ve just published. Try them out, solve them, and share your solutions and comments!

  1. https://gmatclub.com/forum/the-table-sh ... 49367.html
  2. https://gmatclub.com/forum/the-table-li ... 49363.html
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  8. https://gmatclub.com/forum/a-transporta ... 49489.html
  9. https://gmatclub.com/forum/a-report-com ... 49487.html
  10. https://gmatclub.com/forum/for-a-univer ... 49491.html
  11. https://gmatclub.com/forum/a-nutrition- ... 49476.html
  12. https://gmatclub.com/forum/the-table-sh ... 49495.html
  13. https://gmatclub.com/forum/a-museum-ass ... 49484.html
  14. https://gmatclub.com/forum/the-table-sh ... 49500.html
  15. https://gmatclub.com/forum/a-kennel-ass ... 49478.html
  16. https://gmatclub.com/forum/a-food-scien ... 49586.html
  17. https://gmatclub.com/forum/a-regional-b ... 49593.html
  18. https://gmatclub.com/forum/a-european-t ... 49595.html
  19. https://gmatclub.com/forum/a-film-archi ... 49597.html
  20. https://gmatclub.com/forum/the-table-pr ... 49600.html
  21. https://gmatclub.com/forum/the-table-sh ... 49602.html
  22. https://gmatclub.com/forum/samira-is-co ... 49614.html
  23. https://gmatclub.com/forum/the-table-sh ... 49617.html
  24. https://gmatclub.com/forum/the-city-is- ... 49626.html
  25. https://gmatclub.com/forum/eight-food-t ... 49650.html
  26. https://gmatclub.com/forum/eleven-shipp ... 49653.html
  27. https://gmatclub.com/forum/five-robotic ... 49670.html
  28. https://gmatclub.com/forum/the-table-sh ... 49690.html
  29. https://gmatclub.com/forum/the-table-sh ... 49693.html
  30. https://gmatclub.com/forum/the-table-sh ... 49695.html
  31. https://gmatclub.com/forum/the-table-sh ... 49700.html
  32. https://gmatclub.com/forum/the-table-di ... 49706.html
  33. https://gmatclub.com/forum/the-table-pr ... 49708.html

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