mathewhe/aqua_rat huggingface dataset:
Question: In Sam's hanger there are 22 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.
Rationale: Total boxes = 22
Filled with toys = 16
Filled with appliance = 6
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 6 - 3 = 3
Correct Option: C
Answer: (C) 3.
Question: When tossed, a certain six-sided die has an equal probability of landing on any of the six sides. If the die is tossed 4 times, what is the probability that it will land on the same side each time?
(A) 1/12
(B) 1/18
(C) 1/36
(D) 1/216
(E) 1/1296
Rationale: On the first toss, the die will land on one of the sides.
On the second toss, the probability of landing on the same side is 1/6.
On the third toss, the probability of landing on the same side is 1/6.
On the fourth toss, the probability of landing on the same side is 1/6.
P(same side four times)=1/6*1/6*1/6=1/216.
The answer is D.
Answer: (D) 1/216
Question: There are 16 bees in the hive , then 6 more fly. How many bees are there in all?
(A) 7
(B) 33
(C) 22
(D) 17
(E) 25
Rationale: 16+6=22 . Answer is C.
Answer: (C) 22
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.4 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
(A) 24 years
(B) 44 years
(C) 32 years
(D) 64 years
(E) 84 years
Rationale: 32 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 4 = 11
4A + 4 = 9
9(5A + 4)=11(4A + 4)
A = 8
Thomasâ€™s current age = 4A
= 32 years.
C
Answer: (C) 32 years
Question: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in four hours, what fraction of the room can Joseph paint in 20 minutes?
(A) 1/4x
(B) x/(x-12)
(C) (x-4)/12x
(D) x/(x-4)
(E) (x-4)/x
Rationale: Let J be Joseph's rate per hour.
1/x + J = 1/4 of a room per hour
J = 1/4 - 1/x, of a room per hour
In 20 minutes, Joseph can paint 1/3*(1/4-1/x) = 1/12-1/3x = (x-4)/12x
The answer is C.
Answer: (C) (x-4)/12x
Question: The ratio of two quantities is incorrect when written as 10 to 14. How should this ratio be written?
(A) 5:14
(B) 10:7
(C) 20:24
(D) 5:7
(E) It cannot be determined from the information given
Rationale: A ratio should be reduced to the lowest common denominator.
10:14 means 10x:14x which can be written as 5(2):7(2)...
ANSWER:D
Answer: (D) 5:7
Question: If the annual increase in the population of a town is 10% and the present number of people is 13000, what will the population be in 2 years?
(A) 15730
(B) 15240
(C) 12456
(D) 11452
(E) 10002
Rationale: The required population is = 13000 (1 + 10/100)^2
= 13000 * 11/10 * 11/10
= 15730
Answer is A
Answer: (A) 15730
Question: The difference between the simple interest on a certain sum at the rate off 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs. 124.05. What is the principal sum?
(A) Rs. 6000
(B) Rs. 8000
(C) Rs. 12000
(D) Rs. 10000
(E) Rs. 5000
Rationale: Explanation:
Let the sum be P
Compound Interest on P at 10% for 2 years when interest is compounded half-yearly
=P(1+(R/2)/100)2T − P = P(1+(10/2)/100)2×2 − P = P(1+1/20)4 − P = P(21/20)4 − P
Simple Interest on P at 10% for 2 years = PRT/100 = (P × 10 × 2)/100 = P/5
Given that difference between compound interest and simple interest = 124.05
=> P(21/20)4 − P − P/5 = 124.05
=> P[(21/20)4 − 1 − 15] = 124.05
=> P[(194481 − 160000 − 32000)/160000] = 124.05
=> P[2481/160000] = 124.05
=> P = (124.05 × 160000)/2481 = 160000/20 = 8000
Answer: Option B
Answer: (B) Rs. 8000
Question: Three people (1 couple and 1 single) are seated at random in a row of 4 chairs. What is the probability that the couple does not sit together?
(A) 3/7
(B) 1/2
(C) 2/5
(D) 3/4
(E) 5/12
Rationale: The total number of arrangements of 3 people is 4*3*2 = 24
Let's think of the couple as a single unit.
The number of arrangements when the couple sits together is 3*2*2 = 12.
Note that we multiply by 2 because the couple can switch places with each other.
The number of ways the couple won't sit together is 24 - 12 = 12
P(couple won't sit together) = 12/24 = 1/2
The answer is B.
Answer: (B) 1/2
Question: 33 1/3% of 36?
(A) 16
(B) 21
(C) 18
(D) 12 number
(E) 18
Rationale: Explanation:
33 1/3 % = 1/3
1/3 * 36 = 12
Answer: Option D
Answer: (D) 12 number
Question: The number of new words that can be formed by rearranging the letters of the word 'FACEUP' is ?
(A) 720
(B) 719
(C) 220
(D) 178
(E) 266
Rationale: Number of words which can be formed = 6! - 1
= 720 - 1
=719.
Answer:B
Answer: (B) 719
Question: Subtracting 30 from a number, the remainder is one fourth of the number. Find the number?
(A) 29
(B) 88
(C) 40
(D) 28
(E) 27
Rationale: Explanation:
3/4 x = 30 => x = 40
Answer:C
Answer: (C) 40
Question: 6 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
(A) 4
(B) 6
(C) 16
(D) 120
(E) 256
Rationale: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 6
hence ans = 5 factorial = 120
hence D
Answer: (D) 120
Question: In the first hour of a two-hour trip, a car traveled 2d kilometers, and in the second hour of the trip, the car traveled one-half that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
(A)  d
(B)  1/3*d
(C)  1/2*d
(D)  3/4*d
(E)  3/2*d
Rationale: Solution:
Lets look at the information given in the question...
Total time travelled = 2 hrs
Distance travelled first hour = 2d
Distance travelled second hour = d
The question is asking for the avg speed at which the car travels for 2 hrs
We know that avg speed = total distance/total time
Lets place the information given in the question to the formula above = (2d+d)/2
= 3/2*d
We find that option E is the answer as it gives the same expression as found in our calculation above. Answer option E
Answer: (E)  3/2*d
Question: In a apartment, 40% of the people speak English, 40% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/2
(B) 2/3
(C) 2/5
(D) 2/7
(E) 2/9
Rationale: P (E) = 40 / 100 = 4 / 10 , P (H) = 40 / 100 = 4 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (4 / 10) + (4 / 10) - (3 / 10) = 4 / 10 = 1/2
A
Answer: (A) 1/2
Question: Magna Bulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magna Bulk charges m dollars for each crate?
(A) 100bd/m
(B) 100m/(bd)
(C) bd/(100m)
(D) m/(bd)
(E) bd/m
Rationale: crate has = bd magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = 100 m / bd
Answer: B
Answer: (B) 100m/(bd)
Question: 45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 40 meters deep by working for 6 hours?
(A) 75
(B) 80
(C) 50
(D) 35
(E) 40
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 40
x = 80 total workers
80 - 45 = 35
The answer is D.
Answer: (D) 35
Question: About the number of pairs which have 12 as their HCF and 136 as their LCM, the conclusion can be
(A) no pair exist
(B) only two such pairs exist
(C) many such pairs exist
(D) only one such pair exists
(E) None of these
Rationale: Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option: A
Answer: (A) no pair exist
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49 m2
(B) 50 m2
(C) 52 m2
(D) 53.5 m2
(E) 55 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2.
answer :A
Answer: (A) 49 m2
Question: 11 persons are sitting ina row. how many ways can 11persons be arranged in a row such that 3 persons should always be together?
(A) 7!×3!
(B) 7!×2!
(C) 9!×3!
(D) 7!×1!
(E) 6!×2!
Rationale: Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person.
Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9! ways.
We had grouped three persons together. These three persons can be arranged among themselves in 3! ways.
Hence, required number of ways
=9!×3!
C
Answer: (C) 9!×3!
Question: A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ?
(A) 9.8km/hr
(B) 3.6km/hr
(C) 8.9km/hr
(D) 7km/hr
(E) 5.9km/hr
Rationale: given upstream(u) =29km/hr
down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr
Answer is (D)
Answer: (D) 7km/hr
Question: If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
(A) 2
(B) 5
(C) 6
(D) 8
(E) None of these
Rationale: Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
P = 1.
Option E
Answer: (E) None of these
Question: It being given that √ 15 = 3.88, the best approximation to √5/3 is
(A) 0.43
(B) 1.89
(C) 1.29
(D) 1.63
(E) 1.54
Rationale: x = √(5/3) = √(5*3)/(3*3)
= √15 /√ 9
= √15/3
= 3.88/3 = 1.29
Answer is C.
Answer: (C) 1.29
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 4 and 9 slices per customer. How many slices cannot be bought?
(A) 58.
(B) 50.
(C) 67.
(D) 74.
(E) 22.
Rationale: Answer:	Let X pizzas of 4 slices and Y pizzas of 9 slices.
4X + 9Y.
Lets check options wise.
A. 58 => 4(19) + 6(32)
B. 50 => we can't write anything with 4 and 6 series..Lets try 4(1) + 9(5) = 49 , 4(6) + 9(3) = 51 , nothing works out
C. 67 => 4(10) + 9(3)
D. 74 => 4(5) + 9(6)B. 74 => 4(5) + 9(6)
E. 22 => 4(1) + 9(2)
Answer: correct option is B
Answer: (B) 50.
Question: What annual payment will discharge a debt of Rs. 1050 due in 2 years at the rate of 5% compound interest?
(A) 993.2
(B) 551.25
(C) 534.33
(D) 543.33
(E) 564.69
Rationale: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1050
820x + 1050 * 441
x = 564.69
So, value of each installment = Rs. 564.69
Answer: Option E
Answer: (E) 564.69
Question: A group of candidates for two analyst positions consists of six people. If one-third of the candidates are disqualified and three new candidates are recruited to replace them, the number of ways in which the two job offers can be allocated will:
(A) Drop by 40%
(B) Remain unchanged
(C) Increase by 20%
(D) Increase by 40%
(E) Increase by 60%
Rationale: Initially 6 people for 2 positions, meaning
6 - 1st position
5 - 2nd position
Total combinations- 5*6 = 30
Now 1/3rd not qualified, so reduce by 2. Hence, now we have 4+3 candidates for the position.
Same as above, 7*6 for two positions will give 42 combinations. Thus, 42-30/30 = 40% increase;
ANSWER:D
Answer: (D) Increase by 40%
Question: Two numbers X and Y are such that the sum of 5% of X and 4% of Y is two-third of the sum of 6% of X and 8% of Y. Find the ratio of X : Y.
(A) 4:3
(B) 3:2
(C) 1:2
(D) 2:1
(E) 3:5
Rationale: 5% of X + 4% B = 2/3 (6% X + 8% Y)
= 5/100X+4/100Y = 2/3(6/100 X + 8/100 Y)
1/100X = 1/75 Y
X/Y = 100/75 = 4/3
Ratio 4:3
ANSWER A
Answer: (A) 4:3
Question: The ratio of red, yellow, and green jelly beans in a jar is 1:2:3. If the number of jelly beans is increased by 10%, 20%, and 30% respectively, what will be the new ratio?
(A) 11:24:39
(B) 7:19:35
(C) 6:18:29
(D) 4:15:28
(E) 2:11:25
Rationale: The new ratio will be 1.1:2.4:3.9=11:24:39.
The answer is A.
Answer: (A) 11:24:39
Question: If x is the sum of s and t, then which one of the following must equal s – t ?
(A) x-2t
(B) x+2t
(C) x-t
(D) x+t
(E) x/2t
Rationale: Given x= s+t if you subtracts both side with -2t
x-2t = s-t
Answer : A
Answer: (A) x-2t
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in two times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 30 minutes, then how many minutes does it take pump X alone to fill the tank?
(A) 15
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/30 per minute.
(R - V/30)*2T=V=RT.
(R-V/30)*2=R
R=V/15.
It takes pump X 15 minutes to fill the tank.
The answer is A.
Answer: (A) 15
Question: The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 60 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?
(A) 75%
(B) 80%
(C) 104.8%
(D) 150.5%
(E) 180%
Rationale: Let length of each side of square A be 10
Area of A = 10^2 = 100
Since , length of each side of square A is increased by 100 percent to make square B
length of each side of square B = 2*10 = 20
Area of B = 20^2 = 400
Since , length of the side of square B is increased by 60 percent to make square C
length of each side of square C= 1.6*20 = 32
Area of C= 32^2 = 1024
Difference in areas of C and cummulative areas of A and B = 1024 -(400+100) = 524
percent is the area of square C greater than the sum of the areas of squares A and B = (524/500) * 100 % = 104.8%
Answer C
Answer: (C) 104.8%
Question: Sum of two numbers is 35. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
(A) A)5
(B) B)9
(C) C)11
(D) D)22
(E) E)15
Rationale: Explanation:
x + y = 35
2x – 3y = 5
x = 22 y = 13
D)
Answer: (D) D)22
Question: What is the sum of all four digit integers formed using the digits 2, 3, 4 and 5 (repetition is allowed)
(A) 444440
(B) 610000
(C) 666640
(D) 995456
(E) 880000
Rationale: n = 4 * 4 * 4 * 4 = 256
<x> = (5555+ 2222) / 2 = 3888.5
Sum = number of integers x average value
n * <x> = 256 * 3888.5 = 711040
answer = D
Answer: (D) 995456
Question: A committee of three people is to be chosen from 3 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 16
(B) 24
(C) 26
(D) 30
(E) 8
Rationale: Total no of ways of choosing a committee = 6C3 = 20
No of ways to choose first couple = 3C1 = 3
No of ways to choose 1 person from remaining 4 = 4C1 = 4
Total number of ways of choosing a married couple to be in the same committee = 3*4=12
So, no of ways not choosing a married couple = 20-12 =8
ANS:E. 8
Answer: (E) 8
Question: After depositing a check into his checking account, the amount of money in Daniel's checking account increased from $9,090.00 to $9180.90. What was the percentage of the increase?
(A) 2%
(B) 1.5%
(C) 1%
(D) 0.5%
(E) None
Rationale: First we need to figure out how much money Daniel deposited:
=$9180.90-$9,090.00=$90.90
Now we need to determine what percentage $90.90 is of $9,090.00:
90.9/9090*100 =1%
answer is C.
Answer: (C) 1%
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
(A) 22
(B) 12
(C) 98
(D) 27
(E) 14
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
Answer: B
Answer: (B) 12
Question: 100 identical coins each with probability 'pp' showing up heads & tossed. If 0<p<10<p<1 and the probability of heads showing on 50 coins is equal to that ofheads on 51 coins, then the value of pp is?
(A) 50/101
(B) 51/103
(C) 51/101
(D) 63/111
(E) 63/113
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: (C) 51/101
Question: The greatest number of four digits which is divisible by 20,25,30 and 70 is:
(A) 8400
(B) 9200
(C) 9600
(D) 9800
(E) 9960
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 20, 25, 30 and 70 is 2100.
On dividing 9999 by 2100, the remainder is 1599.
Required number (9999 - 1599) = 8400.
Answer: Option A
Answer: (A) 8400
Question: January 1, 2008 is Tuesday. What day of the week lies on Jan. 1, 2009 ?
(A) Monday
(B) wednesday
(C) Thursday
(D) Sunday
(E) None of these
Rationale: Solution
The year 2008 is a leap year. So, it has 2 odd day.
1st day of the year 2008 is Tuesday(Given)
so,1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday. Answer C
Answer: (C) Thursday
Question: How many times are the hands of a clock at right angle in 6 hours?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: In 12 hours, they are at right angles 22 times.
In 6 hours, they are at right angles 11 times. Answer: Option C
Answer: (C) 11
Question: If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
(A) $57.45
(B) $35.42
(C) $60.60
(D) $21.56
(E) $78.45
Rationale: The tip is 20% of what he paid for lunch.
tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10
Total spent
50.50 + 10.10 = $60.60
correct answer is C)$60.60
Answer: (C) $60.60
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
(A) 118
(B) 150
(C) 277
(D) 200
(E) 191
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
Answer: D
Answer: (D) 200
Question: There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
(A) 1/5
(B) 2/3
(C) 3/5
(D) 3/7
(E) 4/9
Rationale: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5
A
Answer: (A) 1/5
Question: In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?
(A) 1 1/4
(B) 1 1/6
(C) 1 1/0
(D) 1 1/5
(E) 1 5/1
Rationale: Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10%
Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.Answer: A
Answer: (A) 1 1/4
Question: David obtained 96, 95, 82, 97 and 95 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
(A) 75
(B) 95
(C) 93
(D) 165
(E) 11
Rationale: Explanation:
Average = (96+ 95+ 82+ 97 + 95 )/ 5 = 465/5 = 93.
Answer:C
Answer: (C) 93
Question: Some of 40%-intensity red paint is replaced with 20% solution of red paint such that the new paint intensity is 20%. What fraction of the original paint was replaced?
(A) 2/5
(B) 2/3
(C) 1/3
(D) 1/2
(E) 1/1
Rationale: Let total paint = 1
Let amount replaced = x
40 (1-x) + 20x = 20
x = 1/1
ANSWER:E
Answer: (E) 1/1
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 6 sec
(B) 7 sec
(C) 2 sec
(D) 1 sec
(E) 5 sec
Rationale: t= 60/36* 18/5 = 6 sec
ANSWER A
Answer: (A) 6 sec
Question: If QUESTION = DOMESTIC what will b code for RESPONSE ?
(A) OMESICEM
(B) HSDUISAH
(C) SSIDFUGD
(D) SDIFUGAU
(E) UIDFGWIW
Rationale: Explanation:
Q U E S T I O N
D O M E S T I C
We can see in the word 'RESPONSE' only R and P are the letters whose code is not given, by having a look on options we can say code for R is O and code for P is S (because common in all options).
Now we can easily code the word 'RESPONSE'as 'OMESICEM'.
Answer : A
Answer: (A) OMESICEM
Question: A coin is tossed three times. What is the probability that there is at the least one tail?
(A) 7/8
(B) 6/7
(C) 1/7
(D) 3/7
(E) 1/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed three times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/8 ; P(T) = 1 - 1/8
= 7/8
Answer: A
Answer: (A) 7/8
Question: A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many days ?
(A) 6 1/2days
(B) 7 1/2days
(C) 8 3/5days
(D) 9 3/5days
(E) 10 1/2 days
Rationale: Explanation:
In this question we having, A's work, B's work and A+B+C work. We need to calculate C's work.
We can do it by,
(A+B+C)'s work - (A's work + B's work).
Let's solve it now:
C's 1 day work =
1/4−(1/16+1/12)=(1/4−7/48)=5/48
So C can alone finish the job in 48/5 days,
Which is =
9 3/5days
Option D
Answer: (D) 9 3/5days
Question: If x^3 > y^2 = z, which of the statements could be true?
I. x < y < z
II. x < z < y
III. y < x < z
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Given : x^3 > y^2 = z
I. x < y < z is not true for x=3, y=2, z=4
II. x < z < y is not true for x=3, y=2, z=4
III. y < x < z is true for x=3, y=2, z=4 i.e. Answers can only be Options E
Answer: option B
Answer: (B) III only
Question: Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 108 seconds. The length of each train is:
(A) 82m
(B) 50m
(C) 72m
(D) 150m
(E) None of these
Rationale: Explanation:
The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s
In 108 secs the total distance traveled is 108x25/9 = 300 m.
Therefore the length of each train is = 300/2 = 150 m.
Answer D
Answer: (D) 150m
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?
(A) 292
(B) 180
(C) 192
(D) 144
(E) 168
Rationale: Let no of passengers in the beginning be X
After first station no passengers=(X-X/3)+280=2X/3 +280
After second station no passengers =1/2(2X/3+280)+12
1/2(2X/3+280)+12=248
2X/3+280=2*236 = 472 - 280 = 192
2X/3=192
X=288. So the answer is option C) 192.
Answer: (C) 192
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 75
(B) 65
(C) 29
(D) 26
(E) 12
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics
= (C + M)/2 = 150/2
= 75.
Answer:A
Answer: (A) 75
Question: 20/25 = 4/5 . which method did you use to determine whether this proportion is true or false?
(A) true
(B) neutral
(C) false
(D) not sure
(E) none
Rationale: 20/25= 4/5 cross multiplication: 20 * 5= 100, 4 * 25 =100,
we see that 100 are not equal to 100. so there is proportion. corrcet answer: (A)
Answer: (A) true
Question: 1, 4, 9, 16, 25, ?
(A) 35
(B) 36
(C) 48
(D) 49
(E) 50
Rationale: The sequence is a series of squares, 12, 22, 32, 42, 52....
Answer : B.
Answer: (B) 36
Question: If f1(x)=f(x)=12xf1(x)=f(x)=12x and fn(x)=f(fn−1(x)fn(x)=f(fn−1(x), then find f5(x)+f10(x)f5(x)+f10(x) where x = 1
(A) 3/9
(B) 3/2
(C) 3/1
(D) 3/3
(E) 3/4
Rationale: f(x) = 12x12x and f(f(x)) = f(12x)f(12x) = 12(12x)12(12x) = x
Similarly f3(x)=f(f2(x))=f(x)=12xf3(x)=f(f2(x))=f(x)=12x and f4(x)=f(f3(x))=f(12x)=12×12x=xf4(x)=f(f3(x))=f(12x)=12×12x=x
Hence fn(x)=12xfn(x)=12x for n = odd and fn(x)=xfn(x)=x for n = even
f5(x)+f10(x)=12x+xf5(x)+f10(x)=12x+x
If x = 1, ⇒12×1+1=3/2
Answer:B
Answer: (B) 3/2