mathewhe/aqua_rat huggingface dataset:
Question: The average age of A, B and C is 26 years. If the average age of A and C is 29 years, what is the age of B in years ?
(A) 19
(B) 35
(C) 20
(D) 32
(E) 21
Rationale: C
20
Age of B = Age of (A + B + C) – Age of (A + C) = 26 × 3 – 29 × 2 = 78 – 58 = 20 years
Answer: (C) 20
Question: If -1<= x <= 2 and 3 <= y <= 8, which of the following represents the range of all possible values of y-x?
(A)  5 <= y-x <= 6
(B)  1 <= y-x <= 5
(C)  1 <= y-x <= 6
(D)  1 <= y-x <= 9
(E)  1 <= y-x <= 10
Rationale: Maximum value of y-x= 8 - (-1)= 9
Minimum value of y-x= 3-2= 1
D mentions the correct range
Answer: (D)  1 <= y-x <= 9
Question: How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together?
(A) 9
(B) 12
(C) 5
(D) 8
(E) 4
Rationale: Answer: Option A
(700 â€“ 300)/42 = 9 22/42 => 9 Numbers
Answer: (A) 9
Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 100. How much did he have with him in the beginning?
(A) Rs 200
(B) Rs 250
(C) Rs 300
(D) Rs 450
(E) Rs 550
Rationale: Suppose the amount in the beginning was Rs ’x’
Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3
Money spent on food = 1/5 of 2x/3 = Rs 2x/15
Balance = 2x/3 - 2x/15 = Rs 8x/15
Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5
Therefore 2x/5 = 100 = 250
ANSWER:B
Answer: (B) Rs 250
Question: A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?
(A) 25.7 years
(B) 28 years
(C) 29.3 years
(D) 28.8 years
(E) 29 years
Rationale: Explanation:
Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to 2/3 of P.
(48 - P) = 2/3 P
5P = 144 => P = 28.8
ANSWER IS D
Answer: (D) 28.8 years
Question: The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Steve and Danny have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies?
(A) $0.32
(B) $0.40
(C) $0.45
(D) $0.48
(E) $0.54
Rationale: If Steve and Danny submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combined no discount cost.
If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer =(B).
Answer: (B) $0.40
Question: 6 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
(A) 19
(B) 20
(C) 30
(D) 33
(E) 34
Rationale: Though 2*(6C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 5, so he'll play 10 matches.
Similarly, second guy has to play with the rest of 4 as his 2 games with the first guy are already played. So he plays 8matches.
This continues like this and the total matches are 10+8+6...+2
10+8+...+2 = 2(5+4+...+1) = 2((5*6)/2) = 5*6 = 30.
ANSWER:C
Answer: (C) 30
Question: Jim is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be Canola oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Jim accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be Canola oil?
(A) 15/29
(B) 5/8
(C) 5/16
(D) 1/2
(E) 13/27
Rationale: Canola oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;
If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are Canola oil --> proportion = 15/29.
Answer: A.
Answer: (A) 15/29
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 57.76, the number of the member is the group is:
(A) 57
(B) 76
(C) 77
(D) 87
(E) 97
Rationale: Money collected =(57.76 x 100) paise = 5776 paise
numbers of members = 5776 squareroot = 76
Answer B
Answer: (B) 76
Question: The sum of the squares of three numbers is 100, while the sum of their products taken two at a time is 48. Their sum is:
(A) 20
(B) 30
(C) 40
(D) 50
(E) None of these
Rationale: x^+y^2+z^2=100
xy+yz+zx=48
as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
so (x+y+z)^2=100+(2*48)
(x+y+z)^2=196
so x+y+z=14
ANSWER:E
Answer: (E) None of these
Question: Find the value of 72519 x 9999 = m?
(A) 434539873
(B) 355797990
(C) 435453490
(D) 725117481
(E) 873430134
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. The children CEF have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 1440
(D) 4320
(E) 4800
Rationale: for such questions , we can treat both as one then total person=5..
these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 6 ways CEF .. so ans =5!*6=720
ans B
Answer: (B) 720
Question: A man gets a simple interest of Rs.200 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
(A) Rs.102.5
(B) Rs.250
(C) Rs.5012.50
(D) Rs.5062.50
(E) None of these.
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.200
(P)(8)(5)/100 = 200
P = 500
C.I on Rs.2P i.e., Rs.1000 at 5% p.a in two years
=1000{ [1 + 5/100]2 - 1} = 1000{ 212 - 202 /202}
= Rs.102.5
ANSWER:A
Answer: (A) Rs.102.5
Question: Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 5, what is the probability that one of the two cards drawn is numbered 3 ?
(A) 1/3
(B) 1/2
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: (3,2) (2,3) (4,1) (1,4) – only 4 possible scenarios for sum to be 5. One from this 4 has already happened.
From this four cases, only in two we have 3. So, the probability is 2 chances out of 4 that the one that occurred had 3: P=2/4.=1/2
Answer: B.
Answer: (B) 1/2
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45kmph. For how many minutes does the bus stop per hour?
(A) 12
(B) 11
(C) 10
(D) 9
(E) 8
Rationale: Explanation:
Speed of the bus excluding stoppages =54 kmph
Speed of the bus including stoppages =45 kmph
Loss in speed when including stoppages =54âˆ’45=9 kmph
â‡’ In 1 hour, bus covers 9 km less due to stoppages.
Hence, time in which the bus stops per hour
= Time taken to cover 9 km
=distance/speed =9/54hour=1/6hour=60/6min=10min
ANSWER IS C
Answer: (C) 10
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 978
(B) 874
(C) 1076
(D) 1176
(E) 1267
Rationale: 80x + 400 = 12(x – 5)
x = 6.76
100 * 6.76 + 400 = 1076
ANSWER:C
Answer: (C) 1076
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
(A) Rs.18390
(B) Rs.10376
(C) Rs.10456
(D) Rs.10364
(E) Rs.10500
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7 = Rs. 10500
Answer:E
Answer: (E) Rs.10500
Question: Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 420 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her five kids?
(A) 8
(B) 9
(C) 3
(D) 21
(E) 10
Rationale: cost of each apple = 4 dollars
Apples that Benny can buy with the amount she has=420/4 = 90.
Apples that each kid gets evenly = 105/5 =21 Apples.
So the answer is D=21
Answer: (D) 21
Question: Akash leaves Chennai at 6am & reaches Bangalore at 10am. Prakash leaves Hyderabad at 8 am and reaches Chennai at 11:30 am. At what time do they cross each other?
(A) 5 : 50am
(B) 7 : 56am
(C) 8 : 56am
(D) 9 : 00am
(E) 9 : 15am
Rationale: Time taken by Akash = 4 h
Time taken by Prakash = 3.5 h
For your convenience take the product of times taken by both as a distance.
Then the distance = 14km
Since, Akash covers half of the distance in 2 hours(i.e at 8 am)
Now, the rest half (i.e 7 km) will be coverd by both prakash and akash
Time taken by them = 7/7.5 = 56 min
Thus , they will cross each other at 8 : 56am.
C
Answer: (C) 8 : 56am
Question: If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 8?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: because n(n+1) is always an even product of even*odd or odd*even factors,
there is a probability of 1 that that it will be divisible by 2,
and, thus, a probability of 1/2 that it will be divisible by 4
and, thus, a probability of 1/4 that it will be divisible by 8
1*1/4=1/4
Answer : A
Answer: (A) 1/4
Question: If x and y are positive integers and 7 + x + y + xy = 21, what is the value of x + y?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Try each answer choices.
For A: 7 + 3 + xy = 21; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)
For B: 7 + 5 + xy = 21; xy = 9 (no combination of xy = 9 and x + y = 5)
For C: 7 + 6 + xy = 21; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)
For D: 7 + 8 + xy = 21; xy = 6 (no combination of xy = 6 and x + y = 8)
For E: 7 + 9 + xy = 21; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)
Therefore, answer C.
Answer: (C) 6
Question: What is greatest positive integer n such that 2^n is a factor of 12^12?
(A) a)10
(B) b)12
(C) c)16
(D) d)24
(E) e)60
Rationale: The given number is 12^12
=(2*2*3)^12
=(2^24)*(3^12)
So the greatest possible value for n such that 2^n can be factor of given number is 24.
Answer D
Answer: (D) d)24
Question: A river 7m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is?
(A) 54996.5
(B) 32296.5
(C) 34996.5
(D) 34996.5
(E) 31255.5
Rationale: Rate of water flow-4kmph--4000/60--66.66 m/min
depth of river--7m
width of river--75m
vol of water per min--66.66 *7*75---34996.5
Answer C
Answer: (C) 34996.5
Question: Express 20 mps in kmph?
(A) 72
(B) 88
(C) 90
(D) 21
(E) 24
Rationale: 20 * 18/5 = 72 kmph
Answer: A
Answer: (A) 72
Question: Five different books (A, B, C, D and E) are to be arranged on a shelf. Books C and D are to be arranged first and second starting from the right of the shelf. The number of different orders in which books A, B and E may be arranged is
(A) 5!
(B) 3!
(C) 2!
(D) 3! * 2!
(E) None
Rationale: Solution
Since books C and D are arranged first and second, only books A, B and E will change order. Therefore it an arrangement problem involving 3 items and the number of different order is given by
3!
Answer B
Answer: (B) 3!
Question: Mike buys 3 cartons of eggs at the store. Each carton has 12 eggs. How many eggs does mike have?
(A) 12
(B) 18
(C) 36
(D) 35
(E) 16
Rationale: 12 eggs x 3 cartons =36 eggs
12 X 3 = 36
C.36
Answer: (C) 36
Question: 24 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
(A) 625
(B) 600
(C) 552
(D) 676
(E) 700
Rationale: we can go in any bus out of the 24 buses.
Hence He can go in 24 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 23 ways.
Total number of ways = 24 x 23 = 552
ANSWER:C
Answer: (C) 552
Question: 3 candidates in an election and received 5136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 48%
(C) 57%
(D) 59%
(E) 61%
Rationale: Total number of votes polled = (5136 + 7636 + 11628) = 24400
So, Required percentage = 11628/24400 * 100 = 48%
B
Answer: (B) 48%
Question: Which of the following number is divisible by 24 ?
(A) 3125712
(B) 3125717
(C) 3125725
(D) 3125736
(E) 3125745
Rationale: 24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
3125736 is divisible by (3 x 8), i.e., 24
D)
Answer: (D) 3125736
Question: In a group of 120 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) 0.1
(B) 0.13
(C) 0.2
(D) 0.25
(E) 0.3
Rationale: Number of people whose age is less than 20 is given by
120 - 90 = 30
Probability P that a person selected at random from the group is less than 20 is gieven by
30 / 120 = 0.25
correct answer D
Answer: (D) 0.25
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
(A) 4:5
(B) 4:7
(C) 5:3
(D) 3:5
(E) 3:5
Rationale: Let 40% of A = 2/3 B. Then,
40A/100 = 2B/3 => 2A/5 = 2B/3
A/B = (2/3 * 5/2) = 5/3
A:B = 5:3.
Answer: C
Answer: (C) 5:3
Question: A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 70, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
(A) 71
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 70 + 77*5x) = 260x+420x+385x = 1065x
total number of students = 15x
average = 1065x/15x = 71
A is the answer
Answer: (A) 71
Question: 4400÷22÷10=?
(A) 43
(B) 20
(C) 24
(D) 25
(E) 32
Rationale: 4400 ÷ 22 = 200
200 ÷ 10 = 20
Answer is B
Answer: (B) 20
Question: If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers
(A) 0
(B) 25
(C) 50
(D) 75
(E) 100
Rationale: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100.
Answer: E.
Answer: (E) 100
Question: A car covers a distance of 640 km in 5 hours. Find its speed?
(A) 104
(B) 288
(C) 271
(D) 276
(E) 128
Rationale: 640/5 = 128 kmph
Answer: E
Answer: (E) 128
Question: Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years.
(A) Rs 1052
(B) Rs 1152
(C) Rs 1252
(D) Rs 1352
(E) None of these
Rationale: Explanation:
S.I. = 956 - 800 = Rs 156
R=156∗100 /800∗3
R=6 1/2%
New Rate = 6 1/2+4
=21/2%
New S.I. = 800×21/2×3100=252
Now amount will be 800 + 252 = 1052
Option A
Answer: (A) Rs 1052
Question: A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area Y covered by the two roads?
(A) 400
(B) 1550
(C) 1575
(D) 1600
(E) 1625
Rationale: Area Covered by Road Along the Length = 5*200 = 1000 Square Meter
Area Covered by Road Along the Width = 5*120 = 600 Square Meter
Common Area in both Roads (where the roads intersect) = Square with Side 5 meter = 5*5 = 25
Total Area of the Roads Y= 1000+600-25 = 1575
Answer: option C
Answer: (C) 1575
Question: Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 5 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
(A) 4 minutes
(B) 2/7 minutes
(C) 32/7 minutes
(D) 224/7 minutes
(E) 28 minutes
Rationale: Pipe A can fill a tank in 32 minutes --> the rate of A = 1/32 tank/minute;
Pipe B can fill the same tank5 times fasterthan pipe A --> the rate of B = 1/32 + 5/32 = 6/32 tank/minute.
Their combined rate = 1/32 + 6/32 = 7/32 tank/minute;
Therefore, A and B can fill the tank in 32/7 minutes.
Answer: C
Answer: (C) 32/7 minutes
Question: Find the unit's digit in 264^102+264^103
(A) zero 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
Answer: (A) zero 0
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/4.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
(A) 5.
(B) 7.
(C) 9.
(D) 10.
(E) 17.
Rationale: We need to get some number which is less than 50 and exactly divisible by 4,5 and 10
Lets take LCM of three balls 4,5 and 10 =20.
The probability of drawing a blue ball is 1/4...For every 8 balls we get 1 BLUE ball then out of 20 balls we get 5 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 20 balls we get 4 REB balls.
The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 20 balls we get 2 GREEN BALLS.
Then out of 20 - ( 5 + 4 + 2 ) = 9 YELLOW balls.
IMO option C is correct.
Answer: (C) 9.
Question: The average age of three boys is 20 years and their ages are in proportion 3:5:7. What is the age in years of the eldest boy?
(A) 6
(B) 9
(C) 28
(D) 24
(E) 21
Rationale: 3x + 5x + 7x = 60
x =4
7x = 28
Answer:C
Answer: (C) 28
Question: If x is less than y by 25% then y exceed x by:
(A) 33.33%
(B) 25%
(C) 75%
(D) 66.66%
(E) None of these
Rationale: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 25(100-25)*100
=33.33%
ANSWER:A
Answer: (A) 33.33%
Question: The ratio 2 : 3 expressed as a percent equals
(A) 12.5%
(B) 40%
(C) 67%
(D) 125%
(E) None
Rationale: Solution
2 : 3	= 2/ 3
= (2 / 3 x 100)%.
= 66.6 %.
Answer C
Answer: (C) 67%
Question: Twenty percent of the women in a college class are science majors, and the non-science majors make up 60% of the class. What percentage of the men are science majors if 40% of the class are men?
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: Science majors make up 0.4 of the class.
60% of the class are women and 0.2*0.6 = 0.12 of the class are female science majors.
Then 0.28 of the class are male science majors.
0.4x = 0.28
x = 0.7 = 70%
The answer is D.
Answer: (D) 70%
Question: The average student age of a certain class which has 30 students is 10. If one student aged 11 go to another class and the age of the class teacher is included the average changes to 11. What is the age of class teacher?
(A) 32
(B) 41
(C) 45
(D) 48
(E) 50
Rationale: Sum of ages of class before replacement= 30x10=300
Sum of ages of class without teacher= 300-11=289
Sum of ages of class after replacement=30x11=330
Age of teacher=330-289=41
Answer: B
Answer: (B) 41
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
(A) 88%
(B) 90%
(C) 80%
(D) 10%
(E) 80%
Rationale: A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer: C
Answer: (C) 80%
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 10% Vermouth by volume. How many ounces of Gin must he add?
(A) n/6
(B) n/3
(C) 3n/5
(D) 5n/6
(E) 8n/4
Rationale: 4 ounces is vermouth
6 ounces of gin...
Total volume 10.
To make vermouth account for 10% of total volume the new volume must be....
x*0.1=4
x=40 ounces....
So now you see that he must add 30 ounces of gin...
Plug in 15 for n in the answer choices and look for answer 30
E
Answer: (E) 8n/4
Question: Find out the C.I on Rs.7000 at 4% p.a. compound half-yearly for 1 1/2 years.
(A) A)Rs.426.45
(B) B)Rs.427.45
(C) C)Rs.428.45
(D) D)Rs.429.45
(E) E)Rs.430.45
Rationale: A = 7000(51/50)3
= 7428.45
7000
-----------
428.45
ANSWER:C
Answer: (C) C)Rs.428.45
Question: How much time will a train of length 420 m moving at a speed of 72 kmph take to cross another train of length 640 m, moving at 36 kmph in the same direction?
(A) 50
(B) 99
(C) 88
(D) 76
(E) 106
Rationale: The distance to be covered = Sum of their lengths = 420 + 640 = 1060 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 1060/10 = 106 sec.
Answer:E
Answer: (E) 106
Question: A car travels first 160 km at 90 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
(A) 71.11
(B) 84.7
(C) 71.1
(D) 71.17
(E) 71.13
Rationale: Car travels first 160 km at 90 km/hr
Time taken to travel first 160 km = distancespeed=160/90
Car travels next160 km at 80 km/hr
Time taken to travel next 160 km = distancespeed=160/80
Total distance traveled = 160+160=2×160
Total time taken = 160/90+160/80
Average speed = Total distance traveled/Total time taken=320/(160/90+160/80)=84.7 km/hr
Answer:B
Answer: (B) 84.7
Question: Employees of a certain company are each to receive a unique 10-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
(A) 145,660
(B) 149,720
(C) 155,420
(D) 161,280
(E) 167,480
Rationale: There are 8! ways to make codes starting with 12.
There are 8! ways to make codes starting with 24.
There are 8! ways to make codes starting with 36.
There are 8! ways to make codes starting with 48.
The number of codes is 4*8! = 161,280.
The answer is D.
Answer: (D) 161,280
Question: Of the diplomats who attended a summit conference: 20 spoke French, 32 did not speak English and 20% of the diplomats spoke neither French nor English. If 10% of the diplomats spoke both French and English, then how many diplomats attended the conference?
(A) 70
(B) 96
(C) 108
(D) 120
(E) 150
Rationale: 2X2 matrix will be the easiest way to calculate this.
Text in black: given statements
Text in red: calculated values
Thus D=120 is the correct answer
Answer: (D) 120
Question: The number of positive integer solutions for the equation x +y +z + t = 10 is
(A) 60
(B) 74
(C) 84
(D) 54
(E) 104
Rationale: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
10-1 C 4-1 = 9C3 = 84
Answer : C
Answer: (C) 84
Question: If two integers x, y (x>y) are selected from -10 to 5 (inclusive), how many possible cases are there?
(A) 105
(B) 120
(C) 190
(D) 210
(E) 240
Rationale: If two integers x, y (x>y) are selected from -10 to 5 (inclusive), how many possible cases are there?
A. 150
B. 180
C. 190
D. 210
E. 240
-->16C2=16*15/2=120. Therefore, the answer is B.
Answer: (B) 120
Question: Eight friends go to watch a movie but only 5 tickets were available. In how many different ways can 5 people sit and watch the movie?
(A) 8C5
(B) 8*7*6*5*4
(C) 5!
(D) 8!/5!
(E) 8*5
Rationale: Choosing 5 out of 8, when order matters P58, or choosing 5 out of 8, without order and then arranging: C58∗5!
Answer: B.
Answer: (B) 8*7*6*5*4