mathewhe/aqua_rat huggingface dataset:
Question: A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 60. When the number of legs was counted, the number totaled up to 160. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.
(A) 16
(B) 20
(C) 24
(D) 28
(E) 32
Rationale: Let x be the number of chickens.
Then 60-x is the number of pigs.
2x+4(60-x)=160
2x=80
x=40 (chickens)
60-x=20 (pigs)
There are 40-20=20 more chickens on the farm.
The answer is B.
Answer: (B) 20
Question: If the sides of a triangle are 26 cm, 25 cm and 10 cm, what is its area?
(A) 120
(B) 110
(C) 130
(D) 140
(E) 125
Rationale: The triangle with sides 26 cm, 25 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 25 * 10 = 125 cm2
Answer: Option E
Answer: (E) 125
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 30 times, A has killed:
(A) 60 birds
(B) 72 birds
(C) 33 birds
(D) 80 birds
(E) 20 birds
Rationale: Let the total number of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B =(3/8)x
Killing shots by A =(1/3)of	(5/8)x=(5/24)x
Shots missed by B =(1/2) of (3/8)x	=(3/16)x
3x/16= 30 or x =(30 x 16)/3= 160.
Birds killed by A =(5x/24)	=(5/24*160)= 33.
Answer is C.
Answer: (C) 33 birds
Question: Each of four different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
(A) 1/8
(B) 1/6
(C) 1/4
(D) 3/8
(E) 1/2
Rationale: Total # of ways to assign the keys to the locks is 4!4!.
C^24 to choose which 2 keys will fit. Other 2 keys can be arranged only one way.
So P=C^24/4!=14
Answer: C.
Answer: (C) 1/4
Question: If the 1st of the month occurs on a Thursday, on which day of the week does the 20th occur?
(A) Wednesday
(B) Saturday
(C) Tuesday
(D) Thursday
(E) Sunday
Rationale: Each weekday is repeated every 7 days. The 20th of the month is 19 days after the 1st. 19 divided by 7 is 2, with a remainder of 5. Therefore, the 20th occurs on whichever day of the week is five days after the day we started on, meaning the 20th is a Tuesday. Answer: C
Answer: (C) Tuesday
Question: The difference of two numbers is 1340. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) A)265
(B) B)280
(C) C)290
(D) D)300
(E) E)310
Rationale: Let the smaller number be x. Then larger number = (x + 1340).
x + 1340 = 6x + 15
5x = 1325
x = 265
Smaller number = 265.
A)
Answer: (A) A)265
Question: How many five digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 3, whithout any of the digits repeating?
(A) 15
(B) 96
(C) 120
(D) 181
(E) 216
Rationale: First step:
We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0,1,2,3,4,5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
{1, 2, 3, 4, 5} and {0, 1, 2, 4, 5}. How many 5 digit numbers can be formed using this two sets:
{1, 2, 3, 4, 5} --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
{0, 1, 2, 4, 5} --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=96
120+96=216
Answer: E.
Answer: (E) 216
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number Q?
(A) 126
(B) 1386
(C) 3108
(D) 308
(E) 13986
Rationale: As we are using digits 1,5, 8 and digits are allowed to repeat. Each of the unit, tenth and hundredth digit can be used by each of three digits.
So,Total possible numbers with these digits=3 X 3 X 3 =27.
First, As we have 27 three digit number, Sum will be for sure more than 2700..Eliminate options A,B,D
Second, If you imagine numbers Q with the given digits 1,5,8. We have numbers like 888,885,855,858,851. Sum is for sure more than 4000.Eliminate option C.
You are left withanswer E.
Answer: (E) 13986
Question: A is twice as good workman as B, and together they complete a work in 5 days. In how many days can the work be complete by B alone?
(A) 35 days
(B) 65 days
(C) 45 days
(D) 75 days
(E) 15 days
Rationale: B=3A
15 days
E
Answer: (E) 15 days
Question: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY2?
(A) 1/4
(B) 5/6
(C) 4/5
(D) 7/3
(E) 2/7
Rationale: If a number is divisible by 2 the last 2 digits of the number has to be divisible by 2
If the number ends with 12: Number of possibilities = 3 * 2 * 1 = 6
number ends with 14: Possibilities = 6
number ends with 32: Possibilities = 6
number ends with 34: Possibilities = 6
number ends with 24: Possibilities = 6
Total number of possibilities with restriction = 6 *5 =30
Total number of possibilities without restriction = 5! = 120
Probability = 30/120 = 1/4
Answer: A
Answer: (A) 1/4
Question: Two numbers are in the ratio of 15:11. If their H.C.F. is 13, find the numbers.
(A) 195,143
(B) 185,133
(C) 175,123
(D) 165,113
(E) None of them
Rationale: Let the required numbers be 15.x and llx.
Then, their H.C.F. is x. So, x = 13.
The numbers are (15 x 13 and 11 x 13) i.e., 195 and 143.
Answer is A.
Answer: (A) 195,143
Question: You enter a weight loss challenge game and manage to lose 15% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?
(A) 13.3%
(B) 9.22%
(C) 9%
(D) 14%
(E) 12%
Rationale: (100%-15%)*(100%+2%) = 0.85*1.02 = 13.3%
The weigh in records your weight loss at 13.3%!
The Answer is A
Answer: (A) 13.3%
Question: Score Interval Number of Scores
50-59 2
60-69 10
70-79 15
80-89 27
90-99 18
The table shows a distribution of test scores. Which score interval contains the median of the 72 scores?
(A) a) 60-69
(B) b) 70-79
(C) c) 80-89
(D) d) 90-99
(E) e) Cannot determine.
Rationale: 36th person
80-89 C
Answer: (C) c) 80-89
Question: A box contains2 blue marbles, 4 red marble, 3 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either green or yellow?
(A) 5/11
(B) 4/11
(C) 3/11
(D) 2/11
(E) 1/11
Rationale: Given that there are 2 blue marbles, 4 red marbles, 3 green marbles and 2 yellow marbles. Probability that both marbles are green = 3Câ‚‚/11Câ‚‚ = 3/55
Probability that both are yellow = Â²Câ‚‚/11Câ‚‚ = 1/55
Probability that one green and other is yellow = (3Câ‚ * Â²Câ‚)/11Câ‚‚ = 6/55
Required probability = 3/55 + 1/55 + 6/55
= 10/55=2/11
Answer:D
Answer: (D) 2/11
Question: Let C represent a set of four distinct prime numbers. If the sum of the numbers in C is even and x is a member of C, then what is the least possible value that x can be?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: We are told that C is a set of four distinct prime numbers, and the sum of the numbers in C is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of C must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
Answer: (C) 3
Question: The total age of A & B is 12 years more than the total age of B & C. C is how many year younger than A.
(A) C is 12 years younger than A
(B) C is 12 years younger than B
(C) C is 12 years younger than C
(D) C is 12 years younger than D
(E) B is 12 years younger than A
Rationale: Explanation:
From the given data A+B = 12+(B+C) A+B-(B+C) = 12 A-C=12 years. C is 12 years younger than A
Answer: A
Answer: (A) C is 12 years younger than A
Question: New age consultants have three consultants Gyani, Medha, and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with with Medha but without Gyani and 3 projects with Gyani but without Medha.
The total number of projects for New age consultants is one less than twice the number of projects in which more than one consultant is involved.
What is the number of projects in which Medha alone is involved?
(A) Uniquely equal to zero
(B) Uniquely equal to 1
(C) Uniquely equal to 4
(D) Cannot be determined uniquely
(E) None of these
Rationale: Explanation :
It is given that all the three consultants are involved in 6 projects together. So put 6 where all the three circles intersect.
Buddhi has 2 projects with Medha but without Gyani. i.e., Medha and Buddhi alone worked in 2 projects.
Also given, Buddi worked on 3 projects with Gyani but without Medha. i.e., Buddi and Gyani alone worked on 3 projects.
Gyani worked with Medha in 14 projects. These two worked together along with Buddhi in 6 projects. So Gyani and Medha alone worked on 14 - 6 = 8 Projects.
Lets us assume, Gyani, Buddhi and Medha alone worked on a, b, c projects.
It was given that The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha involved.
=> a + b = 8 + 6 + 2 + c
=> a + b = 16 + c ------------------ (1)
Also given The total number of projects for New age consultants is one less than twice the number of projects in which more than one consultant is involved.
The projects in which more than 1 consultant involved = 6 + 3 + 2 + 8 = 19.
Total projects = a + b + c + 8 + 3 + 2 + 6 = a + b + c + 19
=> 2 × 19 - 1 = a + b + c + 19.
=> a + b + c = 18.
=> a + b = 18 - c.
Substituting this value in equation (1) we get,
=> 18 - c = 16 + c.
=> c = 1.
Answer : B
Answer: (B) Uniquely equal to 1
Question: If there are 5 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
(A) 32
(B) 24
(C) 56
(D) 44
(E) 80
Rationale: Firstly, there are 5 ways to choose 3 groups from the 4 groups. Hence 5C3.
Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.
Hence, the total number of ways are 5C3 * (2^3) = 80
E
Answer: (E) 80
Question: The average expenditure of a man for the first five months is Rs.180 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
(A) Rs.140
(B) Rs.150
(C) Rs.160
(D) Rs.175
(E) none
Rationale: Explanation:
Total income = Rs.(180Ã—5+130Ã—7+290)=Rs.2100
Average monthly income
= Rs. (2100/12)=Rs.175
Correct Option: D
Answer: (D) Rs.175
Question: A train 240 m long passed a pole in 24 seconds. How long will it take to pass a platform 650 m long?
(A) 65 sec
(B) 89 sec
(C) 100 sec
(D) 150 sec
(E) None
Rationale: Sol.
Speed = [240/24] m/sec = 10 m/sec.
∴ Required time = [240 + 650 / 10] sec
= 89 sec.
Answer B
Answer: (B) 89 sec
Question: A girl goes to her school from her house at a speed of 6km/hr and returns at a speed of 4 km/hr. If she takes 10 hours in going and coming back, the distance between her school and house is
(A) 12 kms
(B) 16 kms
(C) 20 kms
(D) 24 kms
(E) None of above
Rationale: Let distance be D10 = D/4 + D/6 Answer : D
Answer: (D) 24 kms
Question: The bankerâ€™s discount on Rs. 1600 at 5% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
(A) 2 months
(B) 4 months
(C) 6 months
(D) 12 months
(E) None
Rationale: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 15%.
âˆ´ Time = [100 * 80 / 1600 * 5] year = 1year = 12 months.
Answer D
Answer: (D) 12 months
Question: If a 36 inches long strip cloth shrinks to 33 inches after being washed, how many inches long will the same strip remain after washing if it were 48 inches long?
(A) 47 inches
(B) 44 inches
(C) 45 inches
(D) 46 inches
(E) None
Rationale: Solution: Shrinking of cloth,
= [(36-33)/36]*100.
= 100/12%
Second time the strip shrinks,
= (48*100)/1200 = 4 inches
hence , the cloth remains = 48-4 = 44.
Answer: Option B
Answer: (B) 44 inches
Question: A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
(A) 10
(B) 99
(C) 72
(D) 26
(E) 81
Rationale: A can do the work in 30/2 i.e., 15 days.
A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10
So A and B together can do the work in 10 days.
Answer: A
Answer: (A) 10
Question: 100 people are attending a newspaper conference. 40 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
(A) 21
(B) 24
(C) 28
(D) 30
(E) 32
Rationale: {Total}={Writers}+{Editors}-{Both}+{Neither}.
{Total}=100;
{Writers}=40;
{Editors}>38;
{Both}=x;
{Neither}=2x;
100=40+{Editors}-x+2x --> x=60-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=60-39=21.
Answer: A.
Answer: (A) 21
Question: How many two-element subsets of <1, 2,3,4,5,6> are there that do not contain the pair of elements 2 and 4?
(A) 11
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: 6C2 - 1 = 14 Answer is C
Answer: (C) 14
Question: What is 10-8+6-4+...+(-14)?
(A)  8
(B)  10
(C)  12
(D)  14
(E)  -2
Rationale: The expression considers all even numbers between 10 and -14 with alternate addition and subtraction of the numbers.
The numbers to be used are: 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, and -14
Now, the first term is positive and the next term is subtracted. So, the required expression becomes,
10 - 8 + 6 - 4 + 2 - 0 + (-2) - (-4) + (-6) - (-8) + (-10) - (-12) + (-14)
= 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14
= 42 - 44
=-2
Hence the correct answer choice is E.
Answer: (E)  -2
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 1170, what will be C's share of the earnings?
(A) $1100
(B) $260
(C) $1080
(D) $1170
(E) $630
Rationale: Explanatory Answer
A, B and C will share the amount of $1170 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $1170 will be 4 : 3 : 2.
Hence, C's share will be 2*1170/9 = 260
correct choice is (B)
Answer: (B) $260
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
(A) 10 kmph
(B) 5 kmph
(C) 20 kmph
(D) 22 kmph
(E) 25 kmph
Rationale: M = 15
S = 5
DS = 15 + 10 = 25
ANSWER:E
Answer: (E) 25 kmph
Question: A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- hours.
(A) 12 hours
(B) 6 hours
(C) 8 hours
(D) 10 hours
(E) 4 hours
Rationale: Explanation :
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12
Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours
Answer : Option A
Answer: (A) 12 hours
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 39
(B) 10
(C) 88
(D) 12
(E) 18
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: (B) 10
Question: Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo?
(A) 9
(B) 11
(C) 24
(D) 48
(E) 54
Rationale: Terry can pick one lunch salad bar....we can choose lettuce 2c1 , tomatoes - 3c1 and olives - 4c1...
Two types of soups , if he picks one then 2c1 ways.
Terry decided to have the combo : Soup + salad...Hmmm...
Using the above information, we get ( 2c1 * 2c1* 3c1 * 4c1 ) = 48..
ANS option D is correct answer..
Answer: (D) 48
Question: s, q, and r are positive integers. If s, q, and r are assembled into the six-digit number sqrsqr, which one of the following must be a factor of sqrsqr?
(A)  23
(B)  19
(C)  17
(D)  7
(E)  none of the above
Rationale: One short way -
sqrsqr = 1000sqr + sqr = (1000+1)sqr = 1001sqr
Therefore any factor of 1001 is a factor of sqrsqr
7 is a factor of 1001
So D
Answer: (D)  7
Question: In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. The total number of family members is
(A) 3
(B) 7
(C) 10
(D) 12
(E) 15
Rationale: 1-1/4 = remain cake 3/4
3/4*3 = 9/4
9/4+1/4 = 10
ANSWER:C
Answer: (C) 10
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are
(A) 39, 30
(B) 41, 32
(C) 42, 33
(D) 43, 34
(E) None of these
Rationale: Solution
Let their marks be (x+9) and x.
Then, x+9	= 56/100(x + 9 +x)
‹=› 25(x+9)
‹=› 14 (2x + 9)
‹=›3x = 99
‹=›x = 33.
SO, their marks are 42 and 33.
Answer C
Answer: (C) 42, 33
Question: If a certain manager had received a 10% raise instead of the 12% raise that she actually received, her salary would have been $60,500. What was her actual salary after the raise?
(A) 55,000
(B) 58,806
(C) 59,290
(D) 59,400
(E) 61,600
Rationale: salary(let X) included 10% increase can be written as
(1+10/100)X=60500
X=60500/1.10------>55000
if there is 12% rise in 55000
then the salary now is 12% of 55000
12*55000/100=6600
then toal salary after increment=55000+6600----->61600
Ans E
Answer: (E) 61,600
Question: Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 + S1. What is the value of K?
(A) 67
(B) 50
(C) 45
(D) 236
(E) 36
Rationale: I used brute force for this question:
S6: 36+30+94=160
S5: 25+25+94=144
S4: 16+20+94=130
S3: 9+15+94=118
S2: 4+10+94=108
S1: 1+5+94=100
S6-S5+S4-S3+S2-S1= 16+12+208=236
Answer D
Answer: (D) 236
Question: What number has a 5:1 ratio to the number 10?
(A) 11
(B) 50
(C) 99
(D) 88
(E) 66
Rationale: 5:1 = x: 10
x = 50
Answer: B
Answer: (B) 50
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 15% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/13
(B) 2/13
(C) 5/20
(D) 6/20
(E) 7/20
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E âˆ© H) = 15 / 100 =
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (3 / 10) + (1 / 5) - (15 / 100) = 35/100 = 7/20
E
Answer: (E) 7/20
Question: The sale price of a trolley bag including the sale tax is Rs. 560. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
(A) Rs 1000
(B) Rs 900
(C) Rs 400
(D) Rs 600
(E) None of these
Rationale: Explanation :
112% of S.P. = 560
S.P. = Rs.(560x 100/112) = Rs.500.
C.P. = Rs (100/125x 500) = Rs 400
Answer : C
Answer: (C) Rs 400
Question: A square, with perimeter 8, is inscribed in a circle. What is the area of the circle?
(A) 36π
(B) 30π
(C) 26π
(D) 2π
(E) 20π
Rationale: Area of circuscribed circle = pi/2*area of square
Area of square = (8/4)^2 = 2^2= 4
Area of circle = pi/2*4=2pi
Answer D
Answer: (D) 2π
Question: There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number?
(A) 25
(B) 66
(C) 77
(D) 88
(E) 44
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 15
3x = 15 => x = 5
=> Smaller number = 5x = 25.
Answer: A
Answer: (A) 25
Question: Find the odd man out. 3, 8, 18, 38, 78, 158, 316
(A) 38
(B) 158
(C) 316
(D) 8
(E) 78
Rationale: Explanation :
3
3 × 2 + 2 = 8
8 × 2 + 2 = 18
18 × 2 + 2 = 38
38 × 2 + 2 = 78
78 × 2 + 2 = 158
158 × 2 + 2 = 318
Hence, 316 is wrong and 318 should have come in place of that
Answer : Option C
Answer: (C) 316
Question: If (x^2 + 1)y=8, which of the following is not a possible value for y?
(A) 8/2
(B) 2/5
(C) 18/3
(D) 3
(E) 17/2
Rationale: Its simple
equation is (x^2 +1)y = 8 ===> x^2 = (8/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (8/y) - 1>= 0 ===> y =< 8. Now only option E has greater value of 'y' than 8.
Thus, correct ans is E
Answer: (E) 17/2
Question: A can eat 10 burgers in 2 days and B can eat 20 burgers in 1 day. For how long will 250 burgers last is both start eating them together?
(A) 25 days
(B) 20 days
(C) 15 days
(D) 10 days
(E) 5 days
Rationale: Explanation:
A can eat 5 burgers in 1 day and B can eat 20 burgers in 1 day
A and B together can eat 25 burgers in 1 day
=>They can eat 250 burgers in 10 days.
Answer: D
Answer: (D) 10 days
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/17
(B) 30/19
(C) 30/11
(D) 30/13
(E) 30/12
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s
= 60/26
= 30/13 hours.
Answer: D
Answer: (D) 30/13
Question: What is the difference between the local values of 4 in the number 54404?
(A) 2992
(B) 3996
(C) 2877
(D) 2077
(E) 1211
Rationale: Explanation:
4000 â€“ 4 = 3996
Answer:B
Answer: (B) 3996
Question: If x/|y| = -2 which of the following must be true?
(A) x = -y
(B) x = y
(C) x = y^2
(D) x^2 =4* y^2
(E) x^3 = y^3
Rationale: x/|y| = -2
x= -2 |y|
Squaring both sides
x^2= (-2 |y|) ^2= 4*y^2
D is the answer
Answer: (D) x^2 =4* y^2
Question: A pipe can fill a cistern in 77 minutes. Find the time in which 1/11 part of the cistern will be filled?
(A) 5min
(B) 2min
(C) 3min
(D) 1min
(E) 7min
Rationale: Full cistern filled in = 77 minutes
1/11 part filled in = 77*1/11 = 7minutes
Answer is E
Answer: (E) 7min
Question: W and X started a business by investing Rs.2100/- and Rs.4900/- respectively. Find the W’s share out of a total profit of Rs.6000:
(A) 1800
(B) 1850
(C) 1900
(D) 1950
(E) 2000
Rationale: W = Rs.2100/-
X = Rs.4900/-
W share 3 parts & X share 7 parts
Total 10 parts -----> Rs.6000/-
----> 1 part -------> Rs.600/-
W share = 3 parts -----> Rs.1800/-
A
Answer: (A) 1800