mathewhe/aqua_rat huggingface dataset:
Question: The distance traveled by Helicopter in one year approximately 750,000,000 miles.The distance traveled by helicopter in 15 years?
(A) 10<4>
(B) 10<6>
(C) 10<7>
(D) 10<9>
(E) 10<16>
Rationale: The distance traveled by Helicopter in one year = 75,000,000 miles
The distance traveled by Helicopter in 15 years =75,000,000 miles * 15 years = 1125000000
= 1125*10<6> (exponent miles) Answer =B
Answer: (B) 10<6>
Question: A does a work in 10days and B does the same work in 15days. In how many days they together will do the same work?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: A+B can finish =AB/A+B = 10*15/(10+15) = 6days
Answer is C
Answer: (C) 6
Question: A set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements?
(A) 2^(2k-2)
(B) 2^(2k) - 2
(C) 2^(2k) -1
(D) 2^(2k)
(E) 2^(2k-1)
Rationale: I used k=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
Avoid 2 since you will get 1 arrangement (k-1) and may be risky since 1 is a number with certain unique properties
Answer: (A) 2^(2k-2)
Question: A box contains 10 tablets of medicine A and 10 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) 19
(E) 21
Rationale: The worst case scenario will be if we remove all 15 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 10+2=12 tablets.
Answer: A.
Answer: (A) 12
Question: Two trains each 170m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 55km/h while the other travels at 50km/h. how long will it take for them to pass each other completely.
(A) 15 sec
(B) 11.6 sec
(C) 31.6 sec
(D) 12.6 sec
(E) 23 sec
Rationale: Explanation:
D = 170 m + 170 m = 340 m
RS = 55 + 50 = 105 * 5/18 = 146/5
T = 340 * 5/146 = 11.6 sec
Answer: Option B
Answer: (B) 11.6 sec
Question: Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 19 boys and 41 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?
(A) 2
(B) 7
(C) 6
(D) 8
(E) 10
Rationale: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.
Table method is shown above; here is how you will use logic:
There are 6 happy boys.
There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.
We have 6 happy boys and 6 sad boys. Total we have 19 boys. So 19 - 6 - 6 = 7 boys must be neither happy nor sad.
Answer (B)
Answer: (B) 7
Question: Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 4,900 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 900 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?
(A) 10.0
(B) 11.0
(C) 13.0
(D) 12.0
(E) 14.0
Rationale: Solution:H stopped 900 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs.
this means she reached there at 11:00.
speed difference between them is 800-500=300 ft/hr
so by the time H stops they have 1500 ft of distance
so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11:00
means 12:00 is the answer.
D
Answer: (D) 12.0
Question: A began business with Rs.36000 and was joined afterwards by B with Rs.54000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
(A) 1
(B) 6
(C) 7
(D) 8
(E) 2
Rationale: 36*12 : 54*x = 2: 1
x = 4
12 -4 = 8
Answer: D
Answer: (D) 8
Question: A district hospital treated 290 patients today, and each of them were either man, woman, or child. If it treated 10 more men than of children, and in equal as many men as women, how many children were treated ?
(A) 90
(B) 80
(C) 100
(D) 110
(E) 70
Rationale: x = the number of men
y = the number of women
z = the number of children
From the first sentence we have
Equation #1: x + y + z = 290
...A district hospital treated 70 more men than children...
Equation #2: x = 10 + z
...in equal as many men as women...
Equation #3: x = y
Now, we can replace x with y in Equation #2
Equation #4: x - z = 10
Now, we can replace x with y in Equation #1
y + y + z = 290
Equation #5: 2y + z = 290
by adding equation #4 and equation #5 we get
x = 100
There are 100 men treated. This is 10 more than the number of children treated, so z = 90. That's the answer. Just as a check, y = 100, and 100 + 100 + 90 = 290.
Answer = 90,(A)
Answer: (A) 90
Question: What annual installment will discharge a debt of Rs. 1008 due in 3 years at 12% simple interest?
(A) 300
(B) 345
(C) 325
(D) 335
(E) None of them
Rationale: Let each Installment be Rs. x
Then, ( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1008
=((28x/25) + (31x/25) + x) = 1008 ïƒ› (28x+31x+25x)=(1008*25)
x= (1008*25)/84 = Rs.300.
Therefore,	Each installment = Rs. 300.
Answer is A.
Answer: (A) 300
Question: The daily wage is increased by 50% and a person now gets Rs 25 per day. What was his daily wage before the increase ?
(A) Rs 20
(B) Rs 16.6
(C) Rs 18
(D) Rs 19
(E) none of these
Rationale: Let A be the daily wages before the increase,
A ( 1 + x/100) = 25 (Given)
Here, x = 50
Therefore, A( 1 + 50/100) = 25
A = (25 x 100) / (150) = Rs 16.6.
ANSWER:B
Answer: (B) Rs 16.6
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is?
(A) 4/15
(B) 4/19
(C) 4/11
(D) 4/13
(E) 4/17
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer: D
Answer: (D) 4/13
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
(A) 16 days
(B) 18 days
(C) 19 days
(D) 11 days
(E) 14 days
Rationale: x/24 + x/30 + x/40 = 1
x = 11 days
Answer:D
Answer: (D) 11 days
Question: In how many ways the word "SCALE" can be arranged?
(A) 220
(B) 240
(C) 120
(D) None
(E) Cannot be determined
Rationale: Explanation :
The required number of ways = 5!
= 120
Answer : C
Answer: (C) 120
Question: How many 3 digit numbers can be formed from the digits 2,3,5,6,7
and 9 which are divisible by 5 and none of the digits is repeated?
(A) 5
(B) 20
(C) 4
(D) 3
(E) 9
Rationale: Since each desired number is divisible by 5,
so we much have 5 at the unit place.
The hundreds place
can now be filled by any of the remaining 4 digits .
so, there4 ways of filling it.
Required number of numbers = (1 * 5 * 4)
= 20
ANSWER B
Answer: (B) 20
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 830 in 4 years. The sum is?
(A) s. 738
(B) s. 638
(C) s. 650
(D) s. 810
(E) s. 735
Rationale: S.I. for 1 year = (830 - 825) = Rs. 5
S.I. for 3 years = 5 * 3 = Rs. 15
Principal = (825 - 15) = Rs. 810.
ANSWER:D
Answer: (D) s. 810
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
(A) 0
(B) 9
(C) 2
(D) 7
(E) 1
Rationale: Average of 20 numbers = 0.
Sum of 20 numbers = (0 * 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).
Answer: A
Answer: (A) 0
Question: If w>0.9, which of the following options can be the value of w?
(A) 0.9^2
(B) √(0.9)
(C) 0.09
(D) 0.9
(E) 0.9^3
Rationale: Lets take a few examples
When .2 is squared it gives .04
when .5 is squared it gives .25
When .9 is squared it gives .81
So raising a fraction to its power of 2 or 3 only reduces the value of the fraction
This is because
.2 = 2/10
.2^2= 4/100
.2^3=8/1000
Since the denominator gets an extra 0 each time u increase the power , it is going to drag the value down
But if you just think about the opposite case :
Then we can see , if squaring a fraction diminish its value, then taking the square root of it will again increase its value
that is √(0.04) will give you back 0.2
so √(0.04) > 0.04
so obviously diminishing the power will appreciate the value
So w √(0.9) > 0.9
Hence Correct Answer is (B)
Answer: (B) √(0.9)
Question: In a class there are 10 boys and 15 girls. In how many ways can a boy and a girl be selected?
(A) 288
(B) 150
(C) 277
(D) 266
(E) 255
Rationale: We can select one boy from 10 boys in 10 ways.
We select one girl from 15 girls in 15 ways
We select a boy and girl in 10 * 15 ways i.e.,
= 150 ways.
Answer: B
Answer: (B) 150
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 70/9 sec
(B) 80/9 sec
(C) 40/9 sec
(D) 60/9 sec
(E) 90/9 sec
Rationale: B
Relative speed = (90 + 72)* 5/18 = 9 * 5 = 45 mps.
The time required = d/s = (100 + 100 + 200)/45
= 400/45 = 80/9 sec.
Answer: (B) 80/9 sec
Question: How many seconds will a 650 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
(A) 48
(B) 36
(C) 26
(D) 39
(E) 18
Rationale: Explanation:
Here distance d = 650 mts
speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s
time t = = 39 sec.
Answer: D
Answer: (D) 39
Question: If ab represents a positive two-digit number, where a and b are one-digit integers, which of the following CAN be true?
(A) a + b = 9
(B) a - b = 9
(C) b - a = 9
(D) Both A and B
(E) Both B and C
Rationale: The (tens place digit, a) cannot be zero, but the (ones place digit, b) can be zero.
A is possible
B is possible
C is NOT possible
Answer: D
Answer: (D) Both A and B
Question: If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a club, or a red jack, or a red queen, or the ten of spades?
(A) 5/13
(B) 7/26
(C) 9/26
(D) 17/52
(E) 19/52
Rationale: There are 13 clubs and 2 red jacks and 2 red queens and 1 ten of spades.
P(club or red jack or red queen or ten of spades) = 18/52 = 9/26
The answer is C.
Answer: (C) 9/26
Question: The average age of the district level hockey team of eleven is 22 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ?
(A) 84 yrs
(B) 34 yrs
(C) 64 yrs
(D) 24 yrs
(E) 44 yrs
Rationale: Explanation:
Total age of players in team = 22 x 11 = 242
When coach is included, total members = 12, Avg age increases by one becomes 23
Total age when coach is included = 23x12 = 276
Age of coach = 276-242 = 34 yrs.
Answer: B
Answer: (B) 34 yrs
Question: A box contains 2 red, 3 black and 4 blue balls. 3 balls are randomly drawn from the box. What is the probability that the balls are of different colors?
(A) 23
(B) 25
(C) 24
(D) 26
(E) 29
Rationale: A box contains 2 red, 3 black and 4 blue balls. 3 balls are randomly drawn from the box. What is the probability that the balls are of different colors?First consider the probability of drawing a red ball at the first draw, a black at the second and a blue at the third. The first probability is 2/9, the second, conditional on the first is 3/8 and the third conditional on the other two is 4/7. The product is (2*3*4)/(9*8*7). It is easy to see that any other order is equally likely (the only difference is the order of the factors in the numerator). So adding 6 equally likely cases we obtain (6*2*3*4)/(9*8*7) = 2/7.
Combinations approach-
Let us assume that all balls are unique.
There are a total of 9 balls.
Total ways = 3 balls can be chosen in 9C3 ways = 9(6!3!) = 9*8*7/3*2*1 = 84
Favorable ways = 1 Red ball, 1 Black ball, and 1 Blue Ball = 2*3*4 = 24
Answer C
Answer: (C) 24
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 11 minutes earlier. How far is the office from his house?
(A) 3 4/5 Km
(B) 3 1/5 Km
(C) 4 1/5 Km
(D) 5 1/5 Km
(E) None
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 19/6
= 24/2 * 19/60
= 19/5 = 3 4/5 Km
A
Answer: (A) 3 4/5 Km
Question: A man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 4
(B) 4.2
(C) 5.3
(D) 1.5
(E) 5.2
Rationale: M = 12
S = x
DS = 12 + x
US = 12 - x
12 + x = (12 - x)2
12 + x = 24 -2x
3x = 12
x = 4
Answer:A
Answer: (A) 4
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?
(A) 240
(B) 480
(C) 720
(D) 1440
(E) 3600
Rationale: In order to sit together they become one entity that instead of having 7 students we have 4+ group of 3 = 4+1= 5 entities. In order to arrange 5 = 5! and the group of 3 can be arranged in 2 ways GAB or BAG hence total possible configurations 240
answer is A
Answer: (A) 240
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/8
(B) 3/2
(C) 3/3
(D) 3/5
(E) 3/7
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: (B) 3/2
Question: A plane flies 500 miles at a speed of r mph. If the plane flies at a speed of r + 250 miles per hour, it would fly the same distance in 1 hour less. What is the value of r?
(A) 250 mph
(B) 200 mph
(C) 205 mph
(D) 300 mph
(E) 425 mph
Rationale: Equation: 500/r = 500/(r+50) + 1
Plug options into the equation
A fits: 500/250 = 500/(250+250) + 1
Answer: A
Answer: (A) 250 mph
Question: Oliver travelled for 15 hours. He covered the first half of the distance at 40 kmph and remaining half of the distance at 45 kmph. Find the distance travelled by Oliver?
(A) 280 km
(B) 634 km
(C) 760 km
(D) 720 km
(E) 612 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/40 + (x/2)/45 = 15 => x/80 + x/90
= 15 => (9x + 8x)/720 = 15 => x
= 720 km
Answer: D
Answer: (D) 720 km
Question: The element being searched for is not found in an array of 100 elements. What is the average number of comparisons needed in a sequential search to determine that the element is not there, if the elements are completely unordered?
(A) 25
(B) 50
(C) 75
(D) 100
(E) 125
Rationale: let us assume k be the element we need to search
then let array be n1,n2,n3..............n100
now to prove that the element searched is not there in the array we have to compare the element K with every element in the array.
So,totally we need 100 comparisons.
ANSWER:D
Answer: (D) 100
Question: If (A+B) = 11, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?
(A) 16.
(B) 8.
(C) 5.
(D) 2.
(E) -2.
Rationale: Given A+B = 11 => A = 11 - B --> Eq 1
B+C = 9
C+D = 3 => D = 3 - C --> Eq 2
Then Eqs 1 + 2 => A + D = 11 - B + 3 - C
=> 14 - (B+C)
=> 14 - 9 = 5.
Option C...
Answer: (C) 5.
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
(A) 76 years
(B) 88 years
(C) 55 years
(D) 10 years
(E) 15 years
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25 => x = 5
Hence, B's age = 2x = 10 years.Answer:D
Answer: (D) 10 years
Question: John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one poetry?
(A) 1/2
(B) 16/45
(C) 3/10
(D) 7/20
(E) 8/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/10*4/9 + 4/10*4/9 = 16/45.
Answer: B.
Answer: (B) 16/45
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
(A) 27%
(B) 70%
(C) 29%
(D) 20%
(E) 50%
Rationale: P = (P*5*R)/100
R = 20%
Answer: D
Answer: (D) 20%
Question: A department of ten people - six men and four women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?
(A) 120
(B) 150
(C) 180
(D) 210
(E) 240
Rationale: They can make a team of 3 men and 2 women.
The number of ways to do this is 6C3*4C2=20*6 = 120
They can make a team of 2 men and 3 women.
The number of ways to do this is 6C2*4C3=15*4 = 60
The total number of distinct groups is 180.
The answer is C.
Answer: (C) 180
Question: A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 15% so that the customer could not buy the required amount of the product. The customer managed to buy only 60% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?
(A) 27%
(B) 29%
(C) 31%
(D) 33%
(E) 35%
Rationale: Let x be the amount of money paid for the first purchase.
The second time, the customer paid 0.6(1.15x)=0.69x.
The difference is 31%.
The answer is C.
Answer: (C) 31%
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 50%
(B) 40%
(C) 60%
(D) 70%
(E) 80%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 x 100 = 50 %
ANSWER:A
Answer: (A) 50%
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 10%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
(A) 32.5
(B) 35
(C) 48
(D) 65
(E) 67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 10%, therefore bringing down the price to $67.5.
4) Now 67.5 has to be added by X % in order to equal the original price.
67.5 + ( X% ) 67.5 = 100.
Solving this eq for X, we get X = 48.1
Answer is C.
Answer: (C) 48
Question: In a certain game of dice, the player’s score is determined as a sum of two throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If John plays this game against 22 other players, what is the probability of the minimum score that will guarantee John some monetary payoff?
(A) 41/50
(B) 1/221
(C) 1/216
(D) 1/36
(E) 1/42
Rationale: To guarantee that John will get some monetary payoff he must score the maximum score of 6+6=12, because if he gets even one less than that so 11, someone can get 12 and John will get nothing.
P(12)=1/6^2=1/36.
Answer: D.
Answer: (D) 1/36
Question: In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
(A) 24
(B) 26
(C) 32
(D) 42
(E) 46
Rationale: Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
answer :A
Answer: (A) 24
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.45000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 2:1
(C) 3:2
(D) 2:3
(E) 4:3
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:45000×9
=45×12:45×9
=3×12:2×9
=4:3
Answer is E.
Answer: (E) 4:3
Question: Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations C of project assignments are possible?
(A) 252
(B) 1,680
(C) 2,340
(D) 362,880
(E) 592,704
Rationale: The ways to select three employees out of 9 for first project = 9C3
The ways to select three employees out of Remaining 6 for Second project = 6C3
Third Project already has the group of three to be assigned to it so need to select that
So total ways to assign 3 employees to each of 3 projects C= 9C3 * 6C3 * 1 = 1,680
Answer: Option B
Answer: (B) 1,680
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 3/21
(B) 1/31
(C) 5/26
(D) 2/25
(E) 1/15
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: Last year, Company X paid out a total of $1,050,000 in salaries to its 43 employees. If no employee earned a salary that is more than 20% greater than any other employee, what is the lowest possible salary that any one employee earned?
(A)  $20,428.01
(B)  $41,667
(C)  $42,000
(D)  $50,000
(E)  $60,000
Rationale: Employee 1 earned $x(say)
Employee 2 will not earn more than $1.2x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 42 employees
(1.2x*42)+x=1,050,000
Solving for x=$20,428.01
Answer A
Answer: (A)  $20,428.01
Question: If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true? I. xy> z^4 II. (x + z)^5 > y III. x+y>z^4
(A) III only
(B) I only
(C) I,III only
(D) II only
(E) II,III only
Rationale: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.
x+y>z^4
Not necessarily true as 1+5<2401
xz>y^4
Not necessarily true as 1.7<625
We don't need to check option as all the options except D can be discarded.
Thus Answer D
Answer: (D) II only
Question: When n liters of fuel was added to a tank that was already 2/3 full, the tank was filled to 8/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?
(A) 10/9 n
(B) 4/3 n
(C) 9/2 n
(D) 9/4 n
(E) 7/3n
Rationale: C is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 2/3 full.
- When n ltr added, it became 8/9
So 2/3 + n = 8/9
n = 8/9 - 6/9
n = 2/9
capacity of the tank is full fraction . i.e. 1 i.e. 9/9
so the question is 9/9 is how much times n
= 9/9 = 1 = xn
so x = 9/2
and total = 9/2n
Answer: (C) 9/2 n
Question: Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $500 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $600 as interest. What was the annual rate of interest?
(A)  5%
(B)  10%
(C)  12%
(D)  4%
(E)  20%
Rationale: First divide $500/2years to get 250$/yr non-compounding interest.
Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $600-$250= $350.
To find the difference in interest gained, $350-$250= $100 increase in interest after the first year through compounding.
From this information we can set up the equation $250 * X% =04% giving us answer choice D.
Answer: (D)  4%