mathewhe/aqua_rat huggingface dataset:
Question: The sum of three consecutive integers is 102. Find the lowest of the three?
(A) 18
(B) 67
(C) 98
(D) 33
(E) 26
Rationale: Three consecutive numbers can be taken as (P - 1), P, (P + 1).
So, (P - 1) + P + (P + 1) = 102
3P = 102 => P = 34.
The lowest of the three
= (P - 1)
= 34 - 1 = 33.
Answer: D
Answer: (D) 33
Question: Every letter in the alphabet has a number value that is equal to its place in the alphabet. Thus, the letter A has a value of 1, the letter B has a value of 2, the letter C has a value of 3, etc... The number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word. What is the number value of the word "CAT"?
(A) 45
(B) 54
(C) 63
(D) 72
(E) 81
Rationale: "CAT" = (3+1+20)*3=72.
The answer is D.
Answer: (D) 72
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.144 in 4 Years?
(A) 5%
(B) 4%
(C) 3%
(D) 9%
(E) 1%
Rationale: 144 = (800*4*R)/100
R = 4%
Answer: B
Answer: (B) 4%
Question: A can finish a work in 12 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
(A) 6
(B) 5
(C) 4
(D) 7
(E) 8
Rationale: B's 10 day's work = ( 1 x 10 ) = 2 .
15 3
Remaining work = ( 1 - 2 ) = 1 .
3 3
Now, 1 work is done by A in 1 day.
12
Therefore 1 work is done by A in ( 12 x 1 ) = 4 days.
C
Answer: (C) 4
Question: If a and b are both even numbers, which of the following is an even number?
(A) a + b+b
(B) a + b + 1
(C) ab+1
(D) ab + 3
(E) NOne
Rationale: Sol.
Sum of two even numbers is always even.
Answer A
Answer: (A) a + b+b
Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
(A) 1961
(B) 1981
(C) 1991
(D) 1971
(E) None of the above
Rationale: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
Answer B
Answer: (B) 1981
Question: There are seven pairs of black shoes and 5 pairs of white shoes .Tey all are put into a box and shoes are drawn at a time.To ensure that at leat one pair of black shoes are taken out,what is the number of shoes required to be drawn out.
(A) 12
(B) 13
(C) 7
(D) 18
(E) 19
Rationale: White shoes: 5*2=10
Black shoes: 7*2=14
Total shoes: 14+10=24
Now, for the worst case,
1st- All the white shoes are taken out, so 10 shoes are drawn.
2nd- All the one sided (assume only left side) black shoes are drawn. So, another 7 shoes are drawn.
So, in the box left shoes are= 24-17=7
Those 7 shoes are right sided black shoes.
So on the 18th draw we'll get the 1st right footed black shoe, i.e. the 1st pair of black shoe.
So, the no. of shoes required to be drawn out is: 18
ANSWER:D
Answer: (D) 18
Question: How many numbers between 1000 and 5000 are exactly divisible by 225?
(A) 16
(B) 18
(C) 19
(D) 12
(E) 13
Rationale: Explanation: First multiple of 225 after 1000 is 1125 (225 × 5 ) and last multiple of 225 before 5000 is 4950 (225 × 22)
Total number are l−a/d+1=4950−1125/225+1=18
Correct Option: B
Answer: (B) 18
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
(A) 4 3/3 km
(B) 4 3/6 km
(C) 4 3/8 km
(D) 4 9/8 km
(E) 7 3/8 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8 = 4 3/8 km
Answer: C
Answer: (C) 4 3/8 km
Question: The radius of a cone is 8 m, height 6 m. Find the slant height?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Cone slant height (l) = √r(power2)+h(power2)
= √64+36 = 10 m.
Answer is B.
Answer: (B) 10
Question: What is the length of a running train P crossing another running train Q?
I.These two trains take 18 seconds to cross each other.
II.These trains are running in opposite directions.
III.The length of the train Q is 180 metres.
(A) I only
(B) II only
(C) III only
(D) All I, II and III are required
(E) Even with I, II and III, the answer cannot be obtained.
Rationale: Explanation:
Let the length of the train P be x metres.
II. These trains are running in opposite directions.
III. Length of the train Q is 180 m.
I.Time taken by P to cross Q = (180 + x)/Relative speed
18 = (180 + x)/Relative speed
Thus, even with I, II and III, the answer cannot be obtained.
Answer is (E).
Answer: (E) Even with I, II and III, the answer cannot be obtained.
Question: In a box, there are 3 blue, 7 white and 4 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?
(A) 4/14
(B) 5/16
(C) 8/32
(D) 2/32
(E) 9/32
Rationale: Total number of bulbs = (3 + 7 + 4) = 14.
Let E = event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.
Therefore, P(E)=4/14
ANSWER:A
Answer: (A) 4/14
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
(A) 19
(B) 27
(C) 29
(D) 47
(E) 28
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18
= 47 min.
Answer:D
Answer: (D) 47
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is?
(A) 16
(B) 18
(C) 17
(D) 12
(E) 12
Rationale: Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 80.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 80 = Rs. 88
Hence, loss % = 12/100 * 100 = 12%
Answer: D
Answer: (D) 12
Question: John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 45 miles per hour, what is v in miles per hour?
(A) 30
(B) 40
(C) 50
(D) 55
(E) 70
Rationale: HiBunuel
THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.
The question is correct. Here's the explanation:
Let distance be D. We can find the total timeequate it, which comes as:
0.8D / 80 + 0.2D / v = D / 40 => v = 40 (Option B).
Answer: (B) 40
Question: Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 9 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?
(A) 8 mph
(B) 5.25 mph
(C) 3.5 mph
(D) 5 mph
(E) 0.5 mph
Rationale: (1 mph +9 mph)/2 = 5 mph
Correct option is: D
Answer: (D) 5 mph
Question: On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 50 percent of the sales representatives prefer to stay at Hotel XYZ and 50 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?
(A) 32
(B) 36
(C) 42
(D) 48
(E) 51
Rationale: 18 people stay in XYZ and 42 people stay in ABC.
30 people want to stay in XYZ and 30 people want to stay in ABC.
Let's put all 30 people who prefer XYZ in hotel ABC.
Then 18 people who prefer ABC will stay in XYZ.
The highest possible number who are not given their preference is 30+18=48.
The answer is D.
Answer: (D) 48
Question: In a certain province in America there are 15 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
(A) 30
(B) 105
(C) 330
(D) 14!
(E) 15!
Rationale: Method-1:
America has Total Cities = 15 and each city should be connected with every other city
So Total Roads required to connect 1st City with other 14 cities = 14
Now 1st City is connected with all other cities so,
So Total Roads required to connect 2nd City with 13 cities (Other than 1st) = 13
Now 1st and 2nd Cities are connected with all other cities so,
So Total Roads required to connect 3rd City with 12 cities (Other than 1st, and 2nd) = 12
......and so on...
Total Roads required = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105=B
Answer: (B) 105
Question: A certain tax rate is $65 per $100.00. What is the rate, expressed as a percent?
(A) 82%
(B) 6.5%
(C) 0.82%
(D) 65%
(E) 0.0065%
Rationale: Here in question it is asking $65 is what percent of $ 100.Suppose $ 65 is x% of 100 means
100* (x/100) = 65
Hence x = 65
So answer is D
Answer: (D) 65%
Question: in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 10 people all together .how many people can sit in a bus?
(A) 52
(B) 49
(C) 91
(D) 88
(E) 66
Rationale: Right Side =15 seat
Left Side =15-3 (3 few seat in right side)= 12 seat
Total= 15+12= 27
People can seat in 27 seat= 27*3=81
People can seat in Last Seat = 10
Total People can seat= 81+10=91
ANSWER:C
Answer: (C) 91
Question: Carl can wash all the windows of his house in 6 hours. His wife Maggie can wash all the windows in 6 hours. How many hours will it take for both of them working together to wash all the windows?
(A) 2
(B) 2 1/4
(C) 3
(D) 4 1/2
(E) 5
Rationale: Work hrs=AB/(A+B)= 36/12 =3
Answer is C
Answer: (C) 3
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 312
Rationale: Explanation:
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
ANSWER IS C
Answer: (C) 322
Question: In "Clash Royal" App Game, Warrior "The Bomber" is a very good defensive options. It can be purchased from the card shop.
The cost of the bomber is quite interesting.
The Cost of 1st bomber is: 2
The Cost of 2nd bomber is: 4
The Cost of 3rd bomber is: 6
The Cost of 4th bomber is: 8
The Cost of 5th bomber is: 10
i.e to buy 5 bombers you need 2+4+6+8+10 = 30 coins.
How many bombers can you buy using 1000 coins ? ?
(A) 47
(B) 53
(C) 62
(D) 71
(E) 75
Rationale: The Cost of 1st bomber is: 2 i.e Total coins spend: 2
The Cost of 2nd bomber is: 4 i.e Total coins spend: 6
The Cost of 3rd bomber is: 6 i.e Total coins spend: 12
The Cost of 4th bomber is: 8 i.e Total coins spend: 20
The Cost of 5th bomber is: 10 i.e Total coins spend: 30
The Cost of 6th bomber is: 12 i.e Total coins spend: 42
The Cost of 7th bomber is: 14 i.e Total coins spend: 56
The Cost of 8th bomber is: 16 i.e Total coins spend: 72
The Cost of 9th bomber is: 18 i.e Total coins spend: 90
The Cost of 10th bomber is: 20 i.e Total coins spend: 110
The Cost of 11th bomber is: 22 i.e Total coins spend: 132
The Cost of 12th bomber is: 24 i.e Total coins spend: 156
The Cost of 13th bomber is: 26 i.e Total coins spend: 182
The Cost of 14th bomber is: 28 i.e Total coins spend: 210
The Cost of 15th bomber is: 30 i.e Total coins spend: 240
The Cost of 16th bomber is: 32 i.e Total coins spend: 272
The Cost of 17th bomber is: 34 i.e Total coins spend: 306
The Cost of 18th bomber is: 36 i.e Total coins spend: 342
The Cost of 19th bomber is: 38 i.e Total coins spend: 380
The Cost of 20th bomber is: 40 i.e Total coins spend: 420
The Cost of 21st bomber is: 42 i.e Total coins spend: 462
The Cost of 22nd bomber is: 44 i.e Total coins spend: 506
The Cost of 23rd bomber is: 46 i.e Total coins spend: 552
The Cost of 24th bomber is: 48 i.e Total coins spend: 600
The Cost of 25th bomber is: 50 i.e Total coins spend: 650
The Cost of 26th bomber is: 52 i.e Total coins spend: 702
The Cost of 27th bomber is: 54 i.e Total coins spend: 756
The Cost of 28th bomber is: 56 i.e Total coins spend: 812
The Cost of 29th bomber is: 58 i.e Total coins spend: 870
The Cost of 30th bomber is: 60 i.e Total coins spend: 930
The Cost of 31st bomber is: 62 i.e Total coins spend: 992
correct answer is C)62
Answer: (C) 62
Question: Which of the following has 12^60 as a factor?
(A) 24^60
(B) 30^40
(C) 40^80
(D) 60^60
(E) 90^80
Rationale: Here 12^60 = 3^60 * 4^60 Only Option A has both .
Smash A
Answer: (A) 24^60
Question: In a group of 150 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
(A) 0.4
(B) 0.5
(C) 0.65
(D) 0.75
(E) 0.85
Rationale: Number of people whose age is less than 20 is given by
150 - 90 = 60
Probability P that a person selected at random from the group is less than 20 is given by
60 / 150 = 0.4
correct answer A
Answer: (A) 0.4
Question: A sum of money doubles itself at compound interest in 15 years. In how many years will it become eight times?
(A) 45 years
(B) 40 years
(C) 42 years
(D) 38 years
(E) None
Rationale: P { 1 + R/100 }^15 = 2P ie [ 1 + R/100]^15 = 2 … (i) Let P[ 1 + R/100]^n = 8P [ 1 + R/100]^n =8 2^3 = { [1 + R/100]15 }^3 [ 1 + R/100]^n = [ 1 + R/100]^45 i.e n=45 Thus required time = 45 years
Answer A
Answer: (A) 45 years
Question: In a school the number of girls is 30% the number of boys. Find the number of boys as a percentage of girls?
(A) 112%
(B) 12%
(C) 333%
(D) 150%
(E) 16%
Rationale: It is given that in a school the number of girls is 30% the number of boys.
If boys=10
girls=3
We are asked for the number of boys as a percentage of girls
b/g=10/3=10 1/3=3.333=333%
Answer is C
Answer: (C) 333%
Question: The average age of 8 men is increased by 2 years. When two of them, whose ages are 20 years and 24 years respectively are replaced by two women. What is the average age of these women?
(A) 36 years
(B) 30 years
(C) 40 years
(D) 42 years
(E) None of these
Rationale: Let the average age of 8 men be X years
Thus, Sum of the ages of 8 men = 8X years
Now, according to the condition of the question, average age of (6 men + 2 women) = (x + 2) years
Thus, Sum of the ages of (6 men + 2 women)
= 8(X + 2) = 8X x 16 years
Hence, it is clear that on replacing two men by two women, sum of their ages increased by 16 years.
Therefore, sum of the ages of two women
= (20 + 24) + 16 = 60 years
Thus, average age of the women = 60/2 = 30 years
ANSWER:B
Answer: (B) 30 years
Question: CONVERT 2.0 hectares in ares
(A) 130 ares.
(B) 160 ares.
(C) 180 ares.
(D) 200 ares.
(E) 250 ares.
Rationale: 2.0 hectares in ares
1 hectare = 100 ares
Therefore, 2.0 hectares = 2.0 × 100 ares
= 200 ares.
ANSWER- D
Answer: (D) 200 ares.
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) Rs.5
(B) Rs.4
(C) Rs.2
(D) Rs.3
(E) Rs.6
Rationale: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: D
Answer: (D) Rs.3
Question: The distance between West-Town to East-Town is 15 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 2 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
(A) 3.
(B) 7.
(C) 10.
(D) 12.
(E) 15.
Rationale: Time taken by the birds to meet = 15/(2 + 1) = 5 mins
Distance traveled by the bird traveling from West-Town = 2 * 5 = 10
Answer: C
Answer: (C) 10.
Question: In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 35, what is the greatest possible value of B x A?
(A) 0
(B) 10
(C) 20
(D) 30
(E) 35
Rationale: I also was confused when I was looking forabove number:D
As far as I understood, 35 is a factor of AB. In other words, the values of B (units digits can be 5 or 0. Better to have option for 5 in this case to havebigger result). Now let's try 35x1 (A=3, B=5 respectively we have =15). But we don't have this number in answer choices, move on. (avoid even multiples of 2,4,6,8 etc (we will have 0 in units thus making our result 0)
35x3 = 105 (A=0 B=5 respectively. Hey! that's 0 now.
35x5= 175 (A=7, B=5 respectively. Increasing trend , we have 35 now). This is the greatest possible value of B x A.
IMO E.
Answer: (E) 35
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVES' is?
(A) 186
(B) 278
(C) 719
(D) 278
(E) 272
Rationale: Number of words which can be formed
= 6! - 1 = 720 - 1
= 719.
Answer:C
Answer: (C) 719
Question: What least number must be substracted from 427398 so that the remaining number is divisible by 15?
(A) 1
(B) 3
(C) 11
(D) 16
(E) 17
Rationale: Solution
On dividing 427398 by 15, we get remainder	= 3.
Required number be substracted
Answer B
Answer: (B) 3
Question: Students of three different classes appeared in common examination. Pass average of 10 students of first class was 50%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
(A) 74%
(B) 75%
(C) 68%
(D) 72%
(E) None
Rationale: Solution:
Sum of pass students of first, second and third class,
= (50% of 10) + (60% of 15)+ (80% of 25)
= 5+9+20 = 34
Total students appeared,
= 10+15+25 = 50
Pass average,
= 34*100/50 = 68%.
Answer: Option C
Answer: (C) 68%
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(8 (x – y) (y – z) (z – x))
is equal to :
(A) 0
(B) 1/12
(C) 3/8
(D) 1/4
(E) 1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(8(x – y) (y – z) (z – x)) = 3/8.
ANSWER:C
Answer: (C) 3/8
Question: A committee of three students has to be formed. There are four candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE
A
Answer: (A) 3
Question: Find the unknown term
8,8,6,2,-4, X
(A) 2
(B) -12
(C) 6
(D) 8
(E) 9
Rationale: 8,8,6,2,-4, X
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
-4 - x should be "8"
-4 - x = 8
x = -12
ANSWER:B
Answer: (B) -12
Question: A person is traveling at 60 km/hr and reached his destiny in 4hr.30m then find the distance?
(A) 150km
(B) 270km
(C) 246km
(D) 196km
(E) 205km
Rationale: T = 4hr30m = 9/2hr
D= T*S = 60*9/2 = 270KM
Answer is B
Answer: (B) 270km
Question: In the particular apartment , 65% reading business magazines at the same time 85% reading fashion magazines.If 70% are reading business magazines then what percentage of people reading fashion magazines?
(A) 75
(B) 36
(C) 65
(D) 28
(E) 37
Rationale: business magazines readers = 65 % ; fashion magazines readers =80% total =70*100 ; business magazines readers = 70 - 65 =5; fashion magazines readers = 100 - 80 =20; total fashion magazines readers = 0.80*20=16; total = 20+16 =36; answer = B
Answer: (B) 36
Question: The sum of 3 consecutive numbers is definitely
(A) Positive.
(B) Divisible by 2.
(C) Divisible by 5.
(D) Divisible by 4.
(E) Divisible by 3.
Rationale: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: E
Answer: (E) Divisible by 3.
Question: Can you think of any three dimensional object that comprises of just two surfaces?
Hint: A piece of paper practically has 6 surfaces as the edges are also counted. Thus if you were thinking of that, it will be a wrong answer.
(A) A cone
(B) A Circle
(C) A Square
(D) A triangle
(E) A dimond
Rationale: A
There is only one possible shape i.e. a cone.
Answer: (A) A cone
Question: In how many ways the letter of the word "Family" can be when F and Y occur together?
(A) 120
(B) 24
(C) 240
(D) 48
(E) 60
Rationale: Consider F and Y as one unit: {FY}.
Now, 5 units {FY}, {A}, {M}, {I}, {L} can be arranged in 5! ways. In addition F and Y within their units can be arranged in 2!. So, the total # of ways is 5!*2!=240.
Answer: C.
Answer: (C) 240
Question: (4.75 x 4.75 x 4.75 + 1.25 x 1.25 x 1.25) / ( 4.75 x 4.75 + 1.25 x 1.25 - 4.75 x 1.25) = ?
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: = (4.753 + 1.253) / (4.752 + 1.253 - 4.75 x 1.25)
now it is same like in the 12th equation (a3 + b3) / (a2 - ab + b2) = a+b
ie. = 4.75 + 1.25 =6
Answer = Option B
Answer: (B) 6
Question: If a person throw 2 dice simultaneously then find the probability of the sum of dots is 3 multiply ?
(A) 1/2
(B) 1/3
(C) 2/5
(D) 7/9
(E) 1/4
Rationale: If 2 dies are thrown E = event of getting a prime number = 12
total number of possible out comes = 36
probability = 12/36 = 1/3
Answer is B
Answer: (B) 1/3
Question: A train ,120 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
(A) 270 m
(B) 255 m
(C) 235 m
(D) 220 m
(E) 240 m
Rationale: Explanation:
Assume the length of the bridge = x meter
Total distance covered = 120+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (120+x)/30 m/s
=> 45 Ã— (10/36) = (120+x)/30
=> 45 Ã— 10 Ã— 30 /36 = 120+x
=> 45 Ã— 10 Ã— 10 / 12 = 120+x
=> 15 Ã— 10 Ã— 10 / 4 = 120+x
=> 15 Ã— 25 = 120+x = 375
=> x = 375-120 =255
Answer: Option B
Answer: (B) 255 m
Question: In how many different number of ways 8 men and 5 women can sit on a shopa which can accommodate persons?
(A) 200
(B) 1716
(C) 230
(D) 250
(E) 270
Rationale: 13p3 = 13 Ã— 12 Ã— 11 = 1716
B)
Answer: (B) 1716
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 18 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 120%
(D) 144%
(E) 138%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,18 = 18/100
x= 80*18/100
x= 14.4
14.4/10 = 1,44 = 144%, Answer D
Answer: (D) 144%
Question: What is the area of square field whose side of length 15 m?
(A) 225 sq m
(B) 286 sq m
(C) 298 sq m
(D) 267 sq m
(E) 231 sq m
Rationale: 15 * 15
= 225 sq m
Answer:A
Answer: (A) 225 sq m
Question: On a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 1,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?
(A) $2.5
(B) $15
(C) $50
(D) $100
(E) $105
Rationale: Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc.
With respect to the problem at hand, at the end of two years, Tim would have
500(1.10)^2 = 500(1.21) = 605
and Lana would have
1,000(1.05)^2 = 1,000(1.1025) =1102.5
Thus, Tim earned 105 dollars, while Lana earned 102.5 dollars
The difference is $2.5 and the answer is A.
Answer: (A) $2.5