mathewhe/aqua_rat huggingface dataset:
Question: How many different ways can 2 students be seated in a row of 8 desks, so that there is always at least one empty desk between the students?
(A)  50
(B)  42
(C)  24
(D)  20
(E)  12
Rationale: 21 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most
two students can be interchanged
21x2=42
B
Answer: (B)  42
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) 20
(B) 10
(C) 5
(D) 15
(E) 25
Rationale: Since, each desired number is divisible by 5, so we must have 5 at the unit place.
So , the tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9)
therefore the 3-digit no can be formed by (5 * 4 * 1) = 20 ways
Ans- A
Answer: (A) 20
Question: A train 200 m long crosses a platform 200 m long in 40 sec; find the speed of the train?
(A) 94 kmph
(B) 58 kmph
(C) 54 kmph
(D) 94 kmph
(E) 36 kmph
Rationale: D = 200 + 200 = 400
T = 40
S = 400/40 * 18/5 = 36 kmph
Answer:E
Answer: (E) 36 kmph
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 22
(B) 23
(C) 40
(D) 88
(E) 99
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C
Answer: (C) 40
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 30 kmph at 8 p.m. from Delhi. When will they meet?
(A) 40.00 a.m.
(B) 10.00 a.m.
(C) 9.48 a.m.
(D) 18.00 a.m.
(E) 19.00 a.m.
Rationale: Explanation:
D = 110 â€“ 20 = 90
RS = 20 + 30 = 50
T = 90/50 = 1 hours 48 minutes
8 a.m. + 1 hours 48 minutes = 9:48 a.m.
Answer: Option C
Answer: (C) 9.48 a.m.
Question: A, B and C enter into a partnership. They invest Rs. 70,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
(A) 21 : 14 : 28
(B) 21 : 16 : 28
(C) 3 : 4 : 2
(D) 21 : 14 : 18
(E) 3 : 4 : 5
Rationale: A : B : C = (70000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 252 : 192 : 336
= 21 : 16 : 28.
Answer: B
Answer: (B) 21 : 16 : 28
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 42 years. What is Deepak present age.
(A) 14
(B) 15
(C) 20
(D) 22
(E) 27
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 6 = 42 => x = 9
So Deepak age is = 3(9) = 27
Option E
Answer: (E) 27
Question: The total weight of six nougat nuggets is 4 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
(A) 0.18 oz.
(B) 0.5 oz.
(C) 0.67 oz.
(D) 5 oz.
(E) 18 oz
Rationale: Average = Total/Number of items
= 4/6 = 0.67.
Hence, C
Answer: (C) 0.67 oz.
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Qâ€™s amount. At the end of the year 25% profit was earned which was equal to 98,000. What was the amount invested by R?
(A) 2,10,000
(B) 1,05,000
(C) 1,75,000
(D) 84,000
(E) None of these
Rationale: Ratio for amount invested by P, Q & R
= 5x Ã— 12 : 6x Ã— 12 : 6x Ã— 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 25% of T
where, T = Total amount
T = 392000
Amount received by
R = 3x /3x+6x+5x(392000)
= 84000
Answer D
Answer: (D) 84,000
Question: The membership of a committee consists of 4 English teachers, 2 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be English teachers?
(A) 2/3
(B) 1/3
(C) 2/9
(D) 1/12
(E) 3/28
Rationale: Probability of first member an English teacher = 3/8
Probability of second member an English teacher = 2/8
Probability of both being english teacher = 3/8x 2/7=3/28 (E)
Answer: (E) 3/28
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 4 to 6. If one of the four staff members worked on the project for 24 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
(A) 60
(B) 90
(C) 120
(D) 192
(E) 180
Rationale: A:B:C:D=2x:3x:4x:6x, for some positive number x. Total time 2x+3x+4x+6x=15x.
If 2x = 24 then 15x = 180;
If 3x = 24 then 15x = 120;
If 4x = 24 then 15x = 90;
If 6x = 24 then 15x = 60;
Only answer choices which is not obtained is 192.
Answer: D.
Answer: (D) 192
Question: Given the following factorials (x+3)!, (x-2)!, and (x+4)! what is the value of x if the greatest common divisor is 720?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 10
Rationale: GCD of (x+3)!, (x-2)!, and (x+4)! is 720. Find x.
Best way to find n is substitute each of the answer and find out the correct one.
I started with A.
Try 8 and find GCD or 11!, 6! and 12!. 6! itself is 720 and 6! which is contained in the other two factorials. This satisfies the condition, hence answer is 7. Also, we can eliminate all other answers as they are less than 7 and n-2 turns out to be less than 5! and hence cannot have a divisor of 120.
Answer is A.
Answer: (A) 8
Question: In year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 35 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 9X/80
(B) 13X/20
(C) 80/9X
(D) 20X/13
(E) 80X/7
Rationale: IMT = 0.25T
JI = 0.35 IMT
0.35 IMT = $x b
IMT = $x/(0.35) b
T = 4*IMT = 4x/0.35 = 4x*100/35 = 80x/7
Ans: "E"
Answer: (E) 80X/7
Question: if price of t.v set is reduced by 18%, then its sale increases by 88%, find net effect on sale value
(A) 44
(B) 54
(C) 46
(D) 47
(E) 48
Rationale: - a + b + ((-a)(b)/100)
= -18+88+(-18*88)/100
= -18+88-16
=54
ANSWER:B
Answer: (B) 54
Question: How many pages do you need if you have to write 150 lines of information into pages that each hold 30 lines?
(A) A)7
(B) B)5
(C) C)9
(D) D)8
(E) E)None of the above
Rationale: Sol.
30 lines per page total 150 lines
= 150 / 30
= 5
Answer : B
Answer: (B) B)5
Question: Which of the following must be true?
1) Every prime number greater than 5 can be written as either as 5n+1 or 5n-1
2) Every prime number greater than 5 can be written as 4n+1 or 4n-1
3) Every number greater than 5 of the form 5n+1 or 5n-1 is a prime number.
(A) 1,2,3
(B) 1,2
(C) 2,3
(D) only 1
(E) only 2
Rationale: Every prime number greater than 3 can be written in the form of 5n+1 or 5n-1 where n is an integer. So 1 can be possible.
3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 5n+1 or 5n-1.
B
Answer: (B) 1,2
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
(A) 2.01
(B) 2.08
(C) 2.065
(D) 2.04
(E) 2.31
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer:A
Answer: (A) 2.01
Question: At a circular table for seven will sit five adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the seven people be arranged around the table.
(A) 16
(B) 24
(C) 32
(D) 48
(E) 64
Rationale: Consider the two parents and two children as one unit.
Then there are three adults and one family unit.
The number of ways 4 can form a line is 4!
Around a circular table, there would be 4 rotations so we divide this number by 4.
There are 3! ways for 4 to sit around the circular table.
Then the two children have two options and the two parents have two options.
Then the total number of ways is 3!*2*2= 24
The answer is B.
Answer: (B) 24
Question: Three partners A, B and C start a business. B's capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Rs 16500 at the end of a year, find out B's share in it.
(A) 2000
(B) 3000
(C) 4000
(D) 5000
(E) 6000
Rationale: Suppose C's capital =x. Then,
B's capital =4x (Since B's capital is four times C's capital)
A's capital =6x (Since twice A's capital is equal to thrice B's capital)
A : B : C =6x:4x:x
= 6 : 4 : 1
B's share
=16500×4/11
=1500×4=6000
Answer is E.
Answer: (E) 6000
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 3?
(A) 3/8
(B) 7/8
(C) 1/8
(D) 1/2
(E) 1/4
Rationale: There are 8 possible outcomes and only one (111) has a sum equal or less than 3.
P(the sum is greater than 3) = 1 - 1/8 = 7/8
The answer is B.
Answer: (B) 7/8
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 14,000?
(A) 50,000
(B) 750,000
(C) 850,000
(D) 1,400,000,000
(E) 750,000,000
Rationale: number of cars sold = x=800000-50y
y=14000
x=800000-700000=100000
revenue from 100000 cars=14000*100000=1400000000 D
Answer: (D) 1,400,000,000
Question: (x + 7) is a factor in x^2 - mx - 35. What is the value of m?
(A) -3
(B) -2
(C) -4
(D) -5
(E) -6
Rationale: I solved the second degree equation and found it like this:
x^2 - mx - 35
(x-5)(x+7)
x=5 or x= -7
Substituting both values for x in the equation we find:
x^2 - mx - 35
=> (-7)^2 - m(-7) = 35
=> 49 + 7m =35
=> 7m = 35-49 = -14
=> m = -2
And with 5, using a similar process we end up with:
(5)^2 - m(5) = 35
-10=5m
m=-2
Ao,ANS B
Answer: (B) -2
Question: If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 22, what is the value of r-p?
(A) 20
(B) 10
(C) 30
(D) 24
(E) 5
Rationale: Arithmetic mean expression for p and q:
(p+q)/2=10 ; p+q=20 ----eq1
Arithmetic mean expression for q and r:
(q+r)/2=20 ; q+r=44 ----eq2
Subtracting eq1 from eq2 we get: r-p=24
Hence, the correct answer is D
Answer: (D) 24
Question: A and B together invested Rs. 12,000 in a business. At the end of the year, out of total profit is Rs. 2,000 B's share was Rs. 500. A's investment was
(A) s. 4,500
(B) s. 9,000
(C) s. 10,500
(D) s. 11,250
(E) s. 12,250
Rationale: A+B=12000
total profit=2000
2000-500=1500
1500;500=3:1
then 3*12000/4=9000
ANSWER:B
Answer: (B) s. 9,000
Question: What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 70 ?
(A) 147
(B) 142
(C) 173
(D) 144
(E) 186
Rationale: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.
Immediate two prime numbers after 70 are - 71 and 73
Sum = 71 + 73 = 144
Answer - D
Answer: (D) 144
Question: In what ratio must rice of Rs.30 per kg be mixed with rice of Rs.56per kg so that cost of mixture is Rs.35 per kg?
(A) 28:15
(B) 6:7
(C) 7:6
(D) 5:21
(E) 21:5
Rationale: (35-56)/(30-35)=6/2=21:5
ANSWER:E
Answer: (E) 21:5
Question: Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2400
(A) 30
(B) 70
(C) 210
(D) 240
(E) 700
Rationale: 27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.
100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.
Then we want to know what is the largest possible GCF of x and 2100.
Well 2400 = 6 * 4 * 10 * 10
We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible.
We know x has one factor of 3, but not two factors --- that takes the 3.
We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other
No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking.
6*4*10 = 240
If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 2100.
D
Answer: (D) 240
Question: One fourth of one third of two fifth of a number is 14. What will be40% of that number
(A) 168
(B) 150
(C) 180
(D) 200
(E) 250
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 14 then x = 14 * 30 = 420
40% of 420 = 168
Answer: Option A
Answer: (A) 168
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 270 m
(E) 290 m
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
ANSWER:D
Answer: (D) 270 m
Question: A and B complete a work in 6 days. A can alone can do it in 10 days. If both can together can do the work in how many days?
(A) 7
(B) 3.75
(C) 2
(D) 1
(E) 8
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
ANSWER B
Answer: (B) 3.75
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) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: T = 60/36 * 18/5
= 6 sec
Answer:D
Answer: (D) 6
Question: 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 32, then how old is B?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 32
5x = 30 => x = 6
Hence, B's age = 2x = 12 years.
ANSWER:E
Answer: (E) 12
Question: At a certain automobile dealership that sells only Tajima's and Franks, the number of non hybrid Tajima's is 35 less than 3 times the number of hybrid Tajima's. 205 total Tajima's are currently owned by the dealership. If the ratio of hybrid Tajima's to non hybrid Franks is 5:4 and there are 280 total automobiles owned by the dealership, how many hybrid Franks are there?
(A) 20
(B) 27
(C) 48
(D) 60
(E) 87
Rationale: First, I only focus on Tajima's. Let x be hybrid Tajima's and y be non hybrid Tajima's. We know that x + y = 205 and we know that y=3x-35, Therefore we can conclude that x= 60 and y= 145
Next, let a be the number of non hybrid franks, we know the ratio, 60/a = 5/4, therefore a=48
Total number of franks is 75, so 75 - 48 = 27
Took me 47 sec
ANSWER:C
Answer: (C) 48
Question: 27 * 27* 27 * 27 = 3^ ?
(A) 7
(B) 12
(C) 5
(D) 6
(E) 8
Rationale: 3^3 * 3^3 * 3^3 * 3^3 = 3^ (3+3+3+3) = 3^12
Answer : 12
Option : B
Answer: (B) 12
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) Rs.345
(B) Rs.270
(C) Rs.275
(D) Rs.324
(E) Rs.525
Rationale: Explanation:
I = (500*9*6)/100 = 270
ANSWER IS B
Answer: (B) Rs.270
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 7/41
(B) 9/42
(C) 3/47
(D) 3/49
(E) None
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
B
Answer: (B) 9/42
Question: How many 1/12s are there in 37 1/2?
(A) 350
(B) 450
(C) 500
(D) 650
(E) 700
Rationale: Required number = (75/2)/(1/12)
= (75/2 x 12/1)
= 450.
ANSWER:B
Answer: (B) 450
Question: Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 10, 20 and 32, what is the minimum possible range in scores of the three test-takers?
(A) 15
(B) 35
(C) 50
(D) 20
(E) 10
Rationale: I simply looked at the 3 different possible scores for each individual test: 10,32,20
We have to find the minimum range:
32-10=22
32-20=12
20-10=10
The find the minimum range, you have to make the set of the 5 scores as small as possible.
Which means that 4 of the 5 scores of each individual person is zero.
10*5 = 50.
Answer:C
Answer: (C) 50
Question: The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is?
(A) 288
(B) 277
(C) 308
(D) 988
(E) 112
Rationale: Other number = (11 * 7700)/275
= 308.
Answer: C
Answer: (C) 308
Question: A test has a mean of 220 and a standard deviation of 10, find the corresponding z score for: a) a test score of 232?
(A) 1.2
(B) 2.4
(C) 5
(D) 5.6
(E) 7
Rationale: A test has a mean of 220 and a standard deviation of 10,
find the corresponding z score for:
a) a test score of 232,
z(232) = (232-220)/10 = 12/10 = 1.2
Option A
Answer: (A) 1.2
Question: A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $168, how many hours overtime did he work?
(A) 8
(B) 21
(C) 14
(D) 12
(E) 15
Rationale: Answer is: B
At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $168 - $120 = $48 Overtime rate (twice regular) = 2 x $3 = $6 per hour => number of overtime hours = $48/$6 = 8
Answer: (A) 8
Question: Nikhilesh invested certain amount in three different schemes A, B and C with the rate of interest 10 p.c.p.a., 12 p.c.p.a.and 15 p.c.p.a. respectively. If the total interest accrued in one year was 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
(A) 8000
(B) 5000
(C) 6500
(D) Cannot be determined
(E) None of these
Rationale: Ratio of Nikhilesh’s investments in different schemes
= 100:150×100/240:150=8:5:12
Now, according to the question,
8k×10/100+5k×12/100+12k×15/100 = 3200
or, 80k + 60k + 180k = 3200 × 100
or, 320k = 3200 × 100
or, k = 1000
∴ amount invested in scheme B will be = 1000 × 5 = 5000
Answer B
Answer: (B) 5000
Question: In a series of consecutive odd numbers, 27 is the sixth smallest number and 25 is the tenth largest number. What is the range of the series?
(A)  32
(B)  26
(C)  28
(D)  16
(E)  14
Rationale: Imp:All are consecutive odd numbers.
27 is the 6th smallest ,there are 5 numbers smaller then 27 ,smallest number :27-10=17
25 is the 10th largest ,so there are 9 numbers larger then 25, largest number:25+18=43
Range:43-17=26
Ans : B
Answer: (B)  26
Question: The H.C.F. of two numbers is 15 and their L.C.M. is 620. If one of the numbers is 375, then the other is:
(A) 36.6
(B) 42.8
(C) 28.4
(D) 11.6
(E) 24.8
Rationale: Other number =	(15 x 620)/375 = 24.8.
ANSWER :E
Answer: (E) 24.8
Question: A couple spent $132 in total while dining out and paid this amount using a credit card. The $132 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food. What was the actual price of the food before tax and tip?
(A) $100
(B) $104
(C) $108
(D) $112
(E) $116
Rationale: Let the price of the meal be x.
After a 10% sales tax addition, the price is 1.1*x
After a 20% tip on this amount, the total is 1.2*1.1*x = 1.32x
1.32x = 132
x = 100
The correct answer is A.
Answer: (A) $100
Question: Three hundred students at College Q study a foreign language. Of these, 160 of those students study French, and 190 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from
(A) 30 to 50
(B) 40 to 100
(C) 60 to 100
(D) 60 to 110
(E) 70 to 110
Rationale: 160 students study French
140 students do not study French
190 students study Spanish
110 students do not study Spanish
90 students study neither French nor Spanish
140-110=30
140-90=50
A. 30 to 50
Answer: (A) 30 to 50
Question: A Bird is flying into the wind going 6 Km/Hr, and with the wind going 26 Km/Hr, What is his Rate?
(A) 10 Km/Hr
(B) 12 Km/Hr
(C) 5 Km/Hr
(D) 15 Km/Hr
(E) 8 Km/Hr
Rationale: DW=26
UW=6
s=?
s= (26-6)/2 = 20 / 2 = 10
Answer = A
Answer: (A) 10 Km/Hr
Question: The diameter of a cylindrical tin is 4cm and height is 5 cm. Find the volume of the cylinder?
(A) 33
(B) 45
(C) 20
(D) 77
(E) 21
Rationale: r = 2 h = 5
π * 2 * 2 * 5 = 20 π cc
Answer:C
Answer: (C) 20
Question: Of the following, which is nearly equal to √12?
(A) 1.5
(B) 2.8
(C) 3.4
(D) 3.5
(E) 4.4
Rationale: Correct answer is 3.5
Let us take the square roots of all the numbers
3.4*3.4=11.56
3.5*3.5=12.25
Difference
12 - 11.56=0.44
12.25 - 12=0.25
Since 0.25 is lesser of both, 3.5 is closer
Answer is D
Answer: (D) 3.5
Question: Half of 2 percent written as decimal is
(A) 5
(B) 0.01
(C) 0.05
(D) 0.005
(E) None of these
Rationale: Explanation:
It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01
Answer: Option B
Answer: (B) 0.01
Question: Three blocks of different colors are to be placed on a row. How many different sitting arrangements are possible if red must be placed next to blue ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Consider red and blue as one. But, in this arrangement they can be placed in two different combinations.
Red first and Blue second or blue first and red second.
Total we have (R and B) and third color = 2 arrangements to do.
Total arrangements= 2*2= 4
B is the answer
Answer: (B) 4
Question: What is the unit digit of (6!*3! / 3!*4!)?
(A) 5
(B) 6
(C) 0
(D) 3
(E) 4
Rationale: (6!*3! /3!*4!)
=(6! / 4!)
=5*6
=30
Units digit of the above product will be equal to 0
Answer C
Answer: (C) 0
Question: Divide Rs. 2800 among A, B and C so that A receives 3/4 as much as B and C together and B receives 1/4 as A and C together. A's share is?
(A) 1300
(B) 1200
(C) 1375
(D) 1400
(E) 8400
Rationale: A+B+C = 2800
A = 3/4(B+C); B = 1/4(A+C)
A/(B+C) = 3/4
A = 1/7 * 8400 => 1200
Answer: B
Answer: (B) 1200
Question: Find the remainder of the division (3^33)/7.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Find the pattern of the remainders after each power:
(3^1)/7 remainder 3
(3^2)/7 remainder 2
(3^3)/7 remainder 6
(3^4)/7 remainder 4
(3^5)/7 remainder 5
(3^6)/7 remainder 1 -->this is where the cycle ends
(3^7)/7 remainder 3 -->this is where the cycle begins again
(3^8)/7 remainder 2
Continuing the pattern to (3^33)/7 gives us a remainder of 6
Final Answer:
E) 6
Answer: (E) 6
Question: Two bullet train s 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
(A) 15.8 sec.
(B) 12.24 sec.
(C) 11.8 sec.
(D) 10.8 sec.
(E) 08.8 sec.
Rationale: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 200) m = 340 m.
Required time = 340x9/250 = 54/5 = 12.24 sec.
ANSWER B
Answer: (B) 12.24 sec.
Question: At what rate percent per annum will a sum of money double in 8 years.
(A) 12.5%
(B) 13.5%
(C) 11.5%
(D) 14.5%
(E) 21.5%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum. Answer: A
Answer: (A) 12.5%
Question: Find the amount on Rs.6000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 5568
(B) 6369
(C) 5460
(D) 5635
(E) 6552
Rationale: 6000 * 104/100 * 105/100
=> 6552
Answer:E
Answer: (E) 6552
Question: The time taken to travel from city X to city Y is 12 hrs.if a person starts at 6 a.m from city x and another person leaves in city y at 8 p.m .when they will meet.
(A) 6 A.M
(B) 7 A.M
(C) 8 A.M
(D) 9 A.M
(E) 10 A.M
Rationale: i-X- 6 A.M 7 A.M 8 A.M 9 A.M 10 A.M 11 A.M 12 P.M 1 P.M 2 P.M 3 P.M 4 5 6 P.M -Y
x- 8 A.M 7 A.M 6 A.M 5 A.M 4 A.M 3 A.M 2 A.M 1 A.M 12 A.M 11 P.M 10 9 8P.M-Y
SO THEY MEET AT 7 A.M
ANSWER:B
Answer: (B) 7 A.M