mathewhe/aqua_rat huggingface dataset:
Question: The cost price of 21 articles is equal to selling price of 18 articles.find gain or loss percentage.
(A) 45/3%
(B) 10/3%
(C) 40/3%
(D) 20/3%
(E) 50/3%
Rationale: Cost Price of each article be Rs 1
Cost Price of 18 articles =Rs18 ,selling price of 18 articles =Rs 21.
Gain%=[(3/18)*100]%=50/3%
Answer is E.
Answer: (E) 50/3%
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
C
Answer: (C) 6
Question: The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places?
(A) 18
(B) 20
(C) 40
(D) 12
(E) 14
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 3! i.e., 24 ways.
Hence the total ways are 2 * 6 = 12.
Answer:D
Answer: (D) 12
Question: Jerry went to a shop and bought things worth Rs. 45, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 21.3
(D) 29.5
(E) 39.7
Rationale: Total cost of the items he purchased = Rs.45
Given that out of this Rs.45, 30 % is given as tax
=> Total tax incurred = 30 % = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (45−30/100−x)6/100 = 30/100
⇒ 6(45 −0.3 −x) = 30
⇒ (45 − 0.3 − x) = 5
⇒ x = 45 − 0.3 − 5 = 39.7
E)
Answer: (E) 39.7
Question: A box contains 10 tablets of medicine A and 16 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.
(A) 12
(B) 15
(C) 17
(D) 18
(E) 21
Rationale: The worst case scenario will be if we remove all 16 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 16+2=18 tablets.
Answer:D.
Answer: (D) 18
Question: The number 189 is equal to the sum of the cubes of two integers. What is the product of those integers?
(A) 8
(B) 15
(C) 20
(D) 27
(E) 39
Rationale: 4^3+ 5^3= 189 the number is 4*5= 20
C
Answer: (C) 20
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 25 miles behind the slower one. How far apart are the two trains at 5 o'clock?
(A) 60 miles
(B) 80 miles
(C) 90 miles
(D) 65 miles
(E) 400 miles
Rationale: Answer = D. 65 miles
Relational speed = 130 - 100 = 30 miles per hour
In 3 hours, difference = 30 * 3 = 90 miles
Fast train trailing 25 miles, so effective difference = 90 - 25 = 65 miles
Answer: (D) 65 miles
Question: A shipment of 8 TV sets contains 6 black and white sets and 2 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?
(A) 1/7
(B) 1/4
(C) 5/14
(D) 11/28
(E) 27/28
Rationale: 2/8 * 1/7 = 2/56
1-(2/56) = 54/56 = 27/28
Answer E
Answer: (E) 27/28
Question: For positive integers x and z, which of the following can be written as z^2?
(A) x^2+1
(B) x^2-1
(C) x^2-24
(D) x^2+11
(E) x^2-11
Rationale: Plug values: if x=6, then 6^2-11=25
The question asks which of the following CAN be written as z^2. If x=6, then x^2-11 CAN be written as 5^2.
Answer: D
Answer: (D) x^2+11
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 457 km
(B) 444 km
(C) 547 km
(D) 645 km
(E) 453 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer:B
Answer: (B) 444 km
Question: 5 nouns, 5 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
(A) 360
(B) 390
(C) 420
(D) 450
(E) 540
Rationale: we have to choose one from each set. 1 from 5 nouns and 1 from 5 verbs and 1 from 3 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
5c1*5c1*3c1*3!=450
ANSWER:D
Answer: (D) 450
Question: The factorial expression 25!/15! is not divisible by which of the following integers?
(A) 31
(B) 12
(C) 16
(D) 17
(E) 19
Rationale: 25!/15! => 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16
(A) 31 None of the Multiplicands present
(B) 12 Can divide 24
(C) 16 Can divide 16
(D) 17 Can divide 17
(E) 19 Can divide 19
Hence answer will be (A)
Answer: (A) 31
Question: 0.002 x 0.6 = ?
(A) 0.0012
(B) 0.001
(C) 0.01
(D) 0.1
(E) NONE OF THESE
Rationale: Explanation:
2 x 6 = 12.
Sum of decimal places = 4
0.002 x 0.6 = 0.0012
Answer- A
Answer: (A) 0.0012
Question: Kate and her boyfriend Ben, completed the painting of their new apartment together in 6 days.If they were to work separately, how long will it take each of them to complete it, if Ben can complete the painting 5 days earlier than Kate.
(A) 6 and 11
(B) 5 and 10
(C) 10 and 15
(D) 8 and 13
(E) 6 and 10
Rationale: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two workers would complete a job in 12 days. This means that (individually) each of them would take MORE than 10 days to do the job.
Answers E, A and C are illogical, since the individual times must both be greater than 10 days.
so we can TEST the values for Answers B and D.
Using the values for Answers C and D...
Answer C: (10)(15)/(10+15) = 150/25 = 6 This is a match
Final Answer:
C
Answer: (C) 10 and 15
Question: A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 12 km, if he completes half of the distance, i.e., (6) km on foot and the other half by running?
(A) 2.6
(B) 2.2
(C) 2.5
(D) 2
(E) 3
Rationale: Required time = (6)/3 + (6)/6 = 3 hours.
Answer:E
Answer: (E) 3
Question: Josh spends a total of $5.00 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?
(A) 91
(B) 100
(C) 101
(D) 109
(E) 140
Rationale: Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=5.0 ---> x+10y=100 ...(1)
Also, x+y=N ...(2)
Solving 1 and 2 , we get, N = 110-9y ---> only value satisfied is when y = 1---> N = 100-9=91.
A is the correct answer. Other options are not equal to multiples of 9 removed from 100.
Answer: (A) 91
Question: If a certain number is divided by 11, the quotient, dividend, and divisor, added together, will amount to 71. What is the number?
(A) 18
(B) 28
(C) 48
(D) 38
(E) 55
Rationale: Let x = the number sought.
Then x/11 + x + 11 = 71
And x = 55.
E
Answer: (E) 55
Question: Three small cruise ships, each carrying 6 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
(A) 1520
(B) 2260
(C) 2870
(D) 3240
(E) 4590
Rationale: The number of ways for the ships to go to the ports is 3! = 6.
At Port A, the number of ways to choose two winners is 6C2 = 15.
At Port B, the number of ways to choose one winner is 6.
At Port C, the number of ways to choose one winner is 6.
The total number of ways to give out gift certificates is 6*15*6*6 = 3240
The answer is D.
Answer: (D) 3240
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) Rs.4580
(B) Rs.4570
(C) Rs.4500
(D) Rs.4550
(E) Rs.2500
Rationale: Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8500
= 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January = Rs.4500
Answer:C
Answer: (C) Rs.4500
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 18 sec
(B) 17 sec
(C) 48 sec
(D) 19 sec
(E) 12 sec
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C
Answer: (C) 48 sec
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
(A)  1:2
(B)  4:5
(C)  1:1
(D)  3:2
(E)  5:3
Rationale: A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2
Answer: (A)  1:2
Question: How many numbers between 200 and 600 are divisible by 4,5 and 6?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Solution
Every such number must be divisible by L.C.M of 4,5,6 i.e, 60.
Such numbers are 240,300,360,420,480,540.
Clearly, there are 6 such numbers.
Answer B
Answer: (B) 6
Question: David bought 4 toys with the average cost of $8. If David also buys the fifth toy with the price of $ 10, what is the average (arithmetic mean) price of those 5 toys?
(A) $5
(B) $6
(C) $8.4
(D) $10
(E) $11
Rationale: 4 toys -> Total cost = 4 * Avg cost = 4*8 = 32
Fifth toy cost = 10
Total cost for 5 toys= 32+10 = 42
AM = 42/5 = 8.4
Hence C
Answer: (C) $8.4
Question: Wanda baked 168 cookies, packaged them in boxes of 12, and sold each box for
$1.20.How many boxes of 12 can be packaged if there are 168 cookies?What was
the total amount of money that Wanda made for all of the boxes sold?
(A) $26.80
(B) $36.80
(C) $46.80
(D) $76.80
(E) $16.80
Rationale: Divide 168 ÷ 12 = 14
Multiply $1.20 x 14 = $16.80
correct answer E
Answer: (E) $16.80
Question: A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
(A) 4:3
(B) 3:4
(C) 2:3
(D) 3:2
(E) 4:5
Rationale: Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×16)
Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3
Answer is A.
Answer: (A) 4:3
Question: The diagonal of a rhombus are 40 m and 30 m. Its area is:
(A) 600
(B) 450
(C) 350
(D) 500
(E) 620
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 40 Ã— 30) Cm(power)2
= 40 Ã— 15 = 600 Cm(power)2
Answer is A.
Answer: (A) 600
Question: If C.P. of 27 books is equal to S.P of 30 books , then your gain or loss is ?
(A) 23 1/3 gain %
(B) 30 10/23 loss %
(C) 10% loss %
(D) 30 1/3 loss %
(E) 40 1/3 loss %
Rationale: Say the cost price of 27 books is $27 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 27$, hence the loss = ($30 - $27)/$30 = 10%.
Answer: C.
Answer: (C) 10% loss %
Question: Of the five numbers in a sequence, the first term is 20,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
(A) 9,375
(B) 9,750
(C) 9,975
(D) 9,984
(E) 19,968
Rationale: 1st number= 20,000
2nd number = 20% of 20,000= 4000
3rd number= 20% of 4000= 800
4th number = 20% of 800= 160
5th number= 20% of 160= 32
Range = 20,000-32= 19968
E is the answer
Answer: (E) 19,968
Question: What quantity of water should taken out to concentrate 24 liters of 40% acidic liquid to 60% acidic liquid?
(A) 5liters
(B) 10liters
(C) 15liters
(D) 8liters
(E) 6liters
Rationale: Required answer is = 24(60-40)/60 = 8 liters
Answer is D
Answer: (D) 8liters
Question: Jane makes toy bears. When she works with an assistant, she makes 90 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
(A) 20%
(B) 80%
(C) 100%
(D) 120%
(E) 200%
Rationale: We can use fractional equivalents here to solve the problem
80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears
10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours
Now we come to productivity
Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour
Hence the productivity is double with the assistant i.e. the increase in productivity is 120%
D
Answer: (D) 120%
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^4 + s^3?
(A) 0
(B) 1
(C) 2
(D) 8
(E) 9
Rationale: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^4+s^3 will have the units digit of 1+9 = 10 as a units digit.
The answer is A.
Answer: (A) 0
Question: If a boat goes 4km upstream in 12 minutes and the speed of the stream is 8 kmph, then the speed of the boat in still water is ?
(A) 28
(B) 29
(C) 30
(D) 31
(E) 32
Rationale: Rate upsteram =(4/12*60)kmph=20kmph.
speed of the stream =8kmph let speed in still water be xkm/hr. then speed upstream=(x-8)km/hr. x-8=20==>x=28km/hr Answer(A)
Answer: (A) 28
Question: A candidate got 35% of the votes polled and he lost to his rival by 2460 votes. How many votes were cast?
(A) 7500
(B) 3388
(C) 2665
(D) 8200
(E) 2661
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2460
100%---------? => 8200
Answer: D
Answer: (D) 8200
Question: 19 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: in case of cycle no of handshakes = no of persons
hence ans = 19
ANSWER:A
Answer: (A) 19
Question: Last year Sandy saved 6% of her annual salary. This year, she made 10% more money than last year, and she saved 10% of her salary. The amount saved this year was what percent of the amount she saved last year?
(A) 133%
(B) 145%
(C) 158%
(D) 170%
(E) 183%
Rationale: Let last year's salary be x.
Last year, Sandy save 0.06x
This year, Sandy saved 0.1*1.1x = 0.11x
0.11x / 0.06x = 11/6 = 1.83 = 183%
The answer is E.
Answer: (E) 183%
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is ?
(A) 17/29
(B) 17/25
(C) 17/265
(D) 17/252
(E) 17/21
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer: B
Answer: (B) 17/25
Question: A woman put $580 into a savings account for one year. The rate of interest on the account was 6½%. How much was the interest for the year in dollars and cents? (Round to the nearest cent)
(A) $37.70
(B) $47.70
(C) $57.70
(D) $67.70
(E) $77.70
Rationale: we have
6 1/2/100=x/580
Multiply the opposites:
6 ½ x 580 = 3770
we take
37.70/3770 .00
100
$37.70
correct answer A
Answer: (A) $37.70
Question: If x/y = 3 and (2a - x)/(5b - y) = 3, then the value of a/b is?
(A)  15/2
(B)  -2
(C)  1
(D)  2
(E)  3
Rationale: x = 3y
2a - 3y = 3(5b - y)
2a - 3y = 15b - 3y
2a = 15b
a/b = 15/2
Answer: A
Answer: (A)  15/2
Question: The labeled price of a table is Rs. 7,000. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
(A) Rs. 5782
(B) Rs. 6195
(C) Rs. 6650
(D) Rs. 7200
(E) None of these
Rationale: Explanation:
Labeled price = Rs. 7,000
By giving 5% discount on labeled price, the selling price is
= 95 / 100 * 7000 = Rs. 6650
By earning 15% profit on the selling of price Rs. 6650 the cost price is
= 100 / 115 * 6650 = Rs. 5782
Therefore, approximate cost is 5782
ANSWER A
Answer: (A) Rs. 5782
Question: There are 18 students in a class. On the day the test was given, Alice was absent. The other 17 students took the test and their average was 78. The next day, Alice took the test, and with this grade included, the new average was 79. What was Alice's grade on the test?
(A) 96
(B) 95
(C) 94
(D) 93
(E) 92
Rationale: 17*78+Alice's grade=18*79
Alice's grade is 18*79-17*78=96.
The answer is A.
Answer: (A) 96
Question: The difference of two numbers is 1097. On dividing the larger number by the smaller, we get 10 as quotient and the 17 as remainder. What is the smaller number ?
(A) 230
(B) 120
(C) 95
(D) 310
(E) 320
Rationale: Solution: Let the smaller number be x. Then larger number = (x + 1097) x + 1097 = 10x + 17 9x = 1080 x = 120
Answer B
Answer: (B) 120
Question: If 0.3 of a number is equal to 0.06 of another number, the ratio of the numbers i
(A) 3 : 15
(B) 1 : 2
(C) 3 : 20
(D) 20 : 3
(E) None
Rationale: Sol.
0.3A = 0.06 B â‡” A / B = 0.06 / 0.30 = 6/30 = 3/15.
âˆ´ A : B = 3 : 15.
Answer A
Answer: (A) 3 : 15
Question: Y can do a work in 2/3 the time it takes X. Z can do the same work in ¾ the time it takes Y.When all three are typing at the same time what fraction of their total work does Y do
(A) 1/3
(B) 4/13
(C) 9/23
(D) 8/29
(E) 9/29
Rationale: given the ratio of the time of y and x is 2/3 : 1
therefore the ratio of speed of the x and y becomes 2 : 3.
similarly the ratio of the speed of the z and y given as 4 : 3
therefore the speed of the y and z becomes 3 : 4.
now , comparing the ratio of the x,y and z
it becomes 2: 3 :: 3 : 4
hence the y is doing 3/9 hence it is doing 1/3 work.
ANSWER:A
Answer: (A) 1/3
Question: An amusement park charges $8 for an adults' ticket, and $6 for a children's ticket. On a certain day, a total of 150 tickets were sold for a total cost of $1020. How many more children's tickets were sold than adults' tickets?
(A) 30
(B) 50
(C) 80
(D) 90
(E) 120
Rationale: ChildCount = ?
AdultCount = ?
TotalCount = 150
ChildAdmission = $6
AdultAdmission = $8
TotalAdmission = $1020
a) TotalCount = AdultCount + ChildCount
b) TotalAdmission = ( ChildAdmission * ChildCount) + (AdultAdmission * AdultCount)
Solve for a) for ChildCount = TotalCount - AdultCount
Substitute into b) :
TotalAdmission = (ChildAdmission * (TotalCount - AdultCount)) + (AdultAdmission * AdultCount)
=> AdultCount = (TotalAdmission - (ChildAdmission * TotalCount)) / (AdultAdmission - ChildAdmission)
So, AdultCount = 60
and ChildCount = 90
So the difference is 30 more children then adults
A. 30
Answer: (A) 30
Question: 40 percent of the members of a study group are women, and 20 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
(A) 0.2
(B) 0.08
(C) 0.16
(D) 0.14
(E) 0.15
Rationale: Say there are 100 people in that group, then there would be 0.4*0.20*100=8 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=8/100.
Answer: B
Answer: (B) 0.08
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3%
(B) 16 2/7%
(C) 16 0/3%
(D) 18 2/3%
(E) 26 2/3%
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: (A) 16 2/3%
Question: Six 6 faced dice are thrown together. The probability that all the three show the same number on them is?
(A) 1/32
(B) 1/7776
(C) 1/33
(D) 1/38
(E) 1/34
Rationale: The three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 = 46656 ways.
Hence the probability is 6/46656
= 1/7776
Answer: B
Answer: (B) 1/7776
Question: power windows: 60%
anti-lock brakes: 25%
CD player: 50%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
(A) 25
(B) 18
(C) 11
(D) 13
(E) 0
Rationale: Answer: D
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 50%, we can set up the following equation:
50=15+22+x
x=13, choiceD.
Answer: (D) 13
Question: If x^4 + y^4 = 300, then the greatest possible value of x is between:
(A) 2 to 3
(B) 5 to 7
(C) 3 to 5
(D) 6 to 8
(E) 10 to 12
Rationale: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.
We're told that X^4 + Y^4 = 300. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....
4^4 = 256
Looking at the answers, it makes sense to see what 4^4 equals....
4^4 = 256
Since that is BELOW 300, and 6^4 will clearly be MORE than 300, we have the correct answer.
Final Answer:
C
Answer: (C) 3 to 5
Question: Series T is a sequence of numbers where each term after the first term is x greater than the term that precedes it. If the sum of the first and last terms of series T is 14, then what is the sum of the first three terms of series T and the last three terms of series T?
(A) -7
(B) 7
(C) 14
(D) 42
(E) 84
Rationale: Since no information is given about the first term, x, and anything else,
assume first term = 1; hence last term = 13,
so, 1 3 5 7 9 11 13 will suffice the series in which x = 2, from here answer is 42
also, 1 2 3 4 5 6 7 8 9 10 11 12 13 also suffices, where x = 1, from which the answer is again 42
ANSWER:D
Answer: (D) 42
Question: A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 1.7 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 0.9
(B) 1.2
(C) 1.5
(D) 1.8
(E) 2.1
Rationale: 72 km/hr = 1.2 km/min
The total distance is 1.8 km.
1.8 / 1.2 = 1.5 minutes
The answer is C.
Answer: (C) 1.5
Question: If in a race of 130m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
(A) 20m
(B) 26m
(C) 11m
(D) 10m
(E) 15m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (130 * 5) / 25 = 26m
Hence, A beats B by 26m.
ANSWER B
Answer: (B) 26m
Question: 12.5 * 5.2 * 8.8 = ?
(A) 352
(B) 435
(C) 224
(D) 646
(E) 572
Rationale: E
572
? = 12.5 * 5.2 * 8.8 = 572
Answer: (E) 572
Question: There are between 130 and 140 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(A) 131
(B) 133
(C) 135
(D) 137
(E) 139
Rationale: The numbers with the form 4n+1 are 133 and 137.
Only 137 has the form 3k+2.
The answer is D.
Answer: (D) 137