mathewhe/aqua_rat huggingface dataset:
Question: 7 people average age is 30. youngest person age is 8. find average of the people when youngest was born.
(A) 23
(B) 24
(C) 25
(D) 22
(E) 27
Rationale: average age of people =30
so have total age =210
before 7 years we have to deduct each person age by seven years 210-56=154
so average age would be 154/7=22
ANSWER:D
Answer: (D) 22
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
(A) 12
(B) 14
(C) 16
(D) 17
(E) 19
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
C)
Answer: (C) 16
Question: At the time of marriage, a man was 10 years elder to his wife. 16 years after their marriage, his age is 6/5 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
(A) 36 years
(B) 16 years
(C) 14 years
(D) 24 years
(E) 10 years
Rationale: let wifes age= x
husband age = x+10
now after 16 years of mrg x+16 wifes age
x+10+12 husbands age
6/5(x+16)=x+10+12
after solving x=14
ANSWER:C
Answer: (C) 14 years
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 14 years
(B) 18 years
(C) 20 years
(D) 22 years
(E) 16 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 22) + 2 = 2(x + 2)
x + 24 = 2x + 4
x = 20.
answer :C
Answer: (C) 20 years
Question: Two pipes P and Q can fill a cistern in 12 and 14 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/2 min
(B) 11 1/4 min
(C) 11 2/4 min
(D) 11 1/5 min
(E) 10 1/2 min
Rationale: 3/12 + x/14 = 1
x= 10 1/2
Answer: E
Answer: (E) 10 1/2 min
Question: For a race a distance of 224 meters can be covered by P in 16 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
(A) 232m
(B) 238m
(C) 224m
(D) 331m
(E) 236m
Rationale: Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/16 = 14m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 16 seconds
Therefore, Distance covered by P in that time= 14m/s x 16 seconds = 224 metres
ANSWER: C
Answer: (C) 224m
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 12?
(A) 5/6
(B) 7/36
(C) 5/36
(D) 1/36
(E) 12/36
Rationale: The sum of numbers appeared is 12.
Therefore, the required probability = n(E)/n(S) = 1/36.
ANSWER:D
Answer: (D) 1/36
Question: If P(32, 6) = kC (32, 6), then what is the value of k?
(A) 6
(B) 32
(C) 120
(D) 720
(E) 820
Rationale: Solution
Since 32P6 = k32C6
⇒ 32!/ ( 32-6 )!= k 32!/ ( 32-6 )!
⇒k = 6! = 720. Answer D
Answer: (D) 720
Question: On a certain planet where people usually tend to live for more than a century, the ratio of present ages of father and son is 7:4. 10 years later, the ratio of their ages will be 5:3. What is the sum of their present ages?
(A) 220
(B) 200
(C) 140
(D) 80
(E) 60
Rationale: The ratio of present ages of father and son is 7:4, so suppose the present ages are 7x and 4x, respectively.
10 years later, the ages of father and son, respectively, shall be 7x + 10 and 4x + 10.
The ratio of ages 10 years later is given to be 5:3.
This means
(7x + 10)/(4x + 10) = 5/3
Solving we get x = 20.
So present age of father is 7x = 140 and present age of son is 4x = 80.
The sum of present ages is thus 220.
Ans A
Answer: (A) 220
Question: Venkat purchased twenty dozens of toys at the rate of 375 per dozen. He sold each one of them at the rate of 33. What was his percentage profit?
(A) 6.5
(B) 5.6
(C) 3.5
(D) 4.5
(E) None of these
Rationale: Cost price of 20 dozen toys = 20 × 375 = 7,500
Selling price of 20 dozen toys = 20 × 33 × 12 = 7,920
Profit percentage = 7920−7500/7500×100=5.6%
Answer B
Answer: (B) 5.6
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.7. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
(A) (0.7)^5
(B) 2(0.7)^4
(C) 3(0.7)^4
(D) 4(0.7)^4(0.3) + (0.7)^5
(E) 5(0.7)^4(0.3) + (0.7)^5
Rationale: P(5 heads) = (0.7)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.7)^4(0.3)
The answer is E.
Answer: (E) 5(0.7)^4(0.3) + (0.7)^5
Question: 1/3 of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the avg speed for the whole journey.
(A) 25.56 kmph
(B) 28.675 kmph
(C) 33.333 kmph
(D) 40.134 kmph
(E) 50.254 kmph
Rationale: Average speed = total distance / total time
LCM = 3, 4 = 12
Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)
= 12/ (4/25 + 3/30+ 5/30
= 150*12/54 = 33.333 kmph
C
Answer: (C) 33.333 kmph
Question: In a basketball game, Dhoni scored 10 points more than Dravid, but only half as many points as Shewag. If the three players scored a combined total of 130 points, how many points did Dhoni score?
(A) 45
(B) 55
(C) 35
(D) 65
(E) 70
Rationale: Let Dravid scored point = x
Then Dhoni Scored = x+10
Shewag Scored = 2*(x+10) = 2x+20
As given, x+x+10+2x+20 = 130 points
4x+30 = 130
x = 130-30/4 = 25
So Dhoni Scored = x +15 i.e) 25+10 = 35
Answer : C
Answer: (C) 35
Question: If P is a prime number greater than 10, what is the remainder when P^2 is divided by 2.
(A) Cannot be determined
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: take square of any prime number
remainder will be 1
Ans B
Answer: (B) 1
Question: In the coordinate plane, a circle centered on point (-3, -3) passes through point (1, 1). What is the area of the circle?
(A) 9π
(B) 32π
(C) 25π
(D) 37π
(E) 41π
Rationale: r^2=(-3-1)^2+(-3-1)^2=16+16=32
Area of circle=πr^2=32π
Answer : B
Answer: (B) 32π
Question: Rahul can done a work in 5 days and meena can done a work in 10 days.In how many days that both are work together?
(A) 3/10
(B) 10/3
(C) 1/3
(D) 5
(E) 6/3
Rationale: A's one day work=1/5
B's one day work=1/10
A+B=1/5+1/10=10+5/50=10/3 days
Ans:option B
Answer: (B) 10/3
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
(A) 1:5
(B) 1:3
(C) 1:1
(D) 1:2
(E) 1:9
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1
Answer: D
Answer: (D) 1:2
Question: At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 40% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
(A) 4/25
(B) 8/23
(C) 2/5
(D) 8/15
(E) 2/5
Rationale: let there be 100 books in all
Historic fiction books = 40% of total = 40
Other books = 60
New historic fiction = 40% of 40 = 16
Other new books = 40% of 60 = 24
total new books = 24+16 = 40
fraction = 16/40 = 2/5
Ans: E
Answer: (E) 2/5
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
(A) Rs.7500
(B) Rs.7200
(C) Rs.6000
(D) Rs.5750
(E) Rs.6750
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
ANSWER:C
Answer: (C) Rs.6000
Question: In how much time will a train of length 140 m, moving at 36 kmph cross an electric pole?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 140/10 = 14 sec.
Answer:D
Answer: (D) sec
Question: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n41?
(A) 100~1,000
(B) 1,000~10,000
(C) 10,000~100,000
(D) 100,000~1,000,000
(E) 1,000,000,000,000~
Rationale: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n41=2^40=(2^10)^4>(10^3)^4=10^12
Thus, the answer is E.
Answer: (E) 1,000,000,000,000~
Question: The ratio between the speeds of two persons is 7:8.If the second main runs 400 km in 4 hours,then find the speed of the another person?
(A) 91.6km/hr
(B) 87.5km/hr
(C) 80.5 km/hr
(D) 92 km/hr
(E) 120.1 km/hr
Rationale: Let the speed of two persons be 7x and 8x km/hr
8x=400/4
x=100/8
x=12.5
Speed of first person=(7*12.5)km/hr
=87.5 km/hr
Answer is option B
Answer: (B) 87.5km/hr
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 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 08 a.m.
(B) 09 a.m.
(C) 12 a.m.
(D) 10 a.m.
(E) 07 a.m.
Rationale: D
10 a.m.
D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: (D) 10 a.m.
Question: In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose 4-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
(A) 174
(B) 171
(C) 186
(D) 196
(E) 200
Rationale: Case 1
1french 3either German or Spanish: 4C1 * 6C3 = 80
Case 2
2french 2either German or Spanish: 4C2 * 6C2 = 90
Case 3
4french 4C4 = 1
Answer is B = 171
Answer: (B) 171
Question: Rectangular tile each of size 80cm by 40cm must be laid horizontally on a rectangular floor of size 130cm by 230cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 6
(B) 2
(C) 8
(D) 9
(E) 7
Rationale: Area of tile = 80*40 = 3200
Area of floor = 130*230 = 29900
No of tiles = 29900/3200 = 9.34
So, the no of tile = 9
ANSWER:D
Answer: (D) 9
Question: There are two numbers. If 60% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) 5/12
(B) 5/7
(C) 5/3
(D) 5/8
(E) 5/1
Rationale: Let the two numbers be x and y.
60/100 * x + y = 5/4y
=> 3/5 x = 1/4 y => x/y
= 5/12
Answer: A
Answer: (A) 5/12
Question: At what rate percent per annum will a sum of money double in 9 years.
(A) 12.5%
(B) 13.5%
(C) 11.5%
(D) 11.1%
(E) 21.5%
Rationale: Let principal = P, Then, S.I.=P and Time=8 years
Rate = [(100 x P)/ (P x 9)]% = 11.1% per annum. Answer: D
Answer: (D) 11.1%
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?
(A) 11
(B) 25
(C) 66
(D) 88
(E) 11
Rationale: 600 --- 400
100 --- ? => 66%
Answer:C
Answer: (C) 66
Question: A certain car dealership offers its newest model in ten exterior and nine interior colors. If the ten interior colors are identical to the nine exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
(A) 45
(B) 81
(C) 90
(D) 10!/2!
(E) 10!
Rationale: I lined up the 10 different colours for Exterion and Interior like this:
E: A B C D E F G H I J
I: A B C D E F G H I J
I calculated the number of combinations: 10*10= 100 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 81.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
B
Answer: (B) 81
Question: Sum of the squares of three numbers is 363 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 22
(C) 25
(D) 27
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 363 + 2* 131
a + b + c = √625 = 25
C
Answer: (C) 25
Question: If a is a positive number and 1/4 the square root of a is equal to 2a, then a =
(A) 1/64
(B) 1/16
(C) 1/2
(D) 4
(E) 16
Rationale: 1/4 of sqrt(a) = 2a, which means that sqrt(a) = 8a
or a = 64a^2 -> divide by a
1=64a
a=1/64
A.
Answer: (A) 1/64
Question: In March, Bill ran an average of 1 mile an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Bill to complete one mile in June?
(A) 3590/60^2
(B) 2410/60^2
(C) 2390/60^2
(D) 3586/60
(E) 60^2/3590
Rationale: Bill ran at an average of 1 mile/hour in march. So to run 1 mile he would take 1 hour = (60 * 60) seconds = 3600 seconds.
If he increases his speed by 10 seconds, he will complete a mile in 3590 seconds. Converting in hours = 3590/(60 * 60) = 3590/(60^2)
ANSWER: A
Answer: (A) 3590/60^2
Question: If positive integers x is even and y is odd, which of the following must be odd?
(A) 2xy
(B) 3x+y-1
(C) x+y
(D) x + y -1
(E) 3(x + y) - 3
Rationale: Let x = 2 and y = 1
2xy = 2*2*1 = 4
3x+y-1 = 3*2 + 1 -1 = 6
x+y = 2+1 = 3
x+y-1 = 2+1-1 = 2
3(x+y) - 3 = 6+3-3 = 6
Answer: C
Answer: (C) x+y
Question: A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
(A) 7 km/hr
(B) 7.2 km/hr
(C) 8 km/hr
(D) 8.2 km/hr
(E) 8.3 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: (B) 7.2 km/hr
Question: Last year the price range (per kg) for 100 varieties of apples in wholesale market was $1,00. If the prices of each of the 100 varieties increased by 10 percent this year over what it was last year, what is the range of the wholesale prices of the 1000 varieties of apples this year?
(A)  $ 50
(B)  $ 100
(C)  $ 110
(D)  $600
(E)  $300
Rationale: let the lowest price be x.
Therefore, highest price is x +100.
Now price of each variety is increased by 10%.
Therefore the price will remain arranged in the same order as before.
or Lowest price = 1.1x and Highest = 1.1 * (x+100)
or Range = highest - lowest = 1.1 * (x+100) - 1.1x
= 110, Hence, C
Answer: (C)  $ 110
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $3,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
(A) $18,400
(B) $19,500
(C) $22,200
(D) $20,400
(E) $21,100
Rationale: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 3500
Net price of the car in 02 = 18700 + 3500 = $22200
Correct Option: C
Answer: (C) $22,200
Question: A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0019)?
(A) 25
(B) 20
(C) 21
(D) 18.81
(E) 22
Rationale: You get 10^2 (100-1) (.0019)
we know 19/10000 = .0019
10^2 (99) * (19/10000)
10^2 = 100 and 100^2 = 10000
Cancel out the 100 with the 10^2
Left with 99(19/100).
0.99*19 = 18.81
Answer : D
Answer: (D) 18.81
Question: Two assembly line inspectors, smithy and glen, inspect widgets as they come off the assembly line. If smithy inspects every fifth widget, starting with the fifth, and glen inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector?
(A) 50
(B) 53
(C) 55
(D) 60
(E) 65
Rationale: Widgets inspected by smithy: ((95-5)/5)+1=18+1=19
Widgets inspected by glen: ((96-3)/3)+1 =31+1 =32
Widgets inspected by both: ((90-15)+1 =6
Total : 19+32 -6=45
hence, widgets not inspected: 98-45=53
Option B
Answer: (B) 53
Question: A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 . The emptying capacity of the tank is 10 per minute heigher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?
(A) 50 m^3/min
(B) 90 m^3/min
(C) 50 m^9/min
(D) 59 m^3/min
(E) 50 m^4/min
Rationale: Explanation:
Let the filling capacity of the pump be x /min.
Then, emptying capacity of the pump=(x+10) /min.
so,
Answer: A) 50 m^3/min
Answer: (A) 50 m^3/min
Question: The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 20 percent of the budget?
(A)  15 °
(B)  36 °
(C)  54 °
(D)  72 °
(E)  150 °
Rationale: 100 percent = 360 degrees
20 percent = 360*20/100 = 72 degrees
Answer is D.
Answer: (D)  72 °
Question: Marts income is 50 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income
(A) 124%
(B) b) 120 %
(C) c) 96 %
(D) d) 90 %
(E) e) 64 %
Rationale: M = (150/100)T
T = (60/100)J
=> M = (90/100)J
Answer D.
Answer: (D) d) 90 %
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 60. He was allowed to drop his lowest score. After doing so, his average test score improved to 65. What is the lowest test score that was dropped?
(A) 20
(B) 45
(C) 55
(D) 65
(E) 80
Rationale: The arithmetic mean of 4 equally weighted tests was 60. So what we can assume is that we have 4 test scores, each 60.
He dropped his lowest score and the avg went to 65. This means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 60.
So the lowest score = 60 - 15 = 45
Answer (B)
Answer: (B) 45
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.
(A) 12
(B) 39
(C) 43
(D) 52
(E) 34
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x - 3).
:. 16 (x - 3) + 87 = 17x or x = (87 - 48) = 39.
Ans: B
Answer: (B) 39
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
(A) 16
(B) 12
(C) 14
(D) 61
(E) 51
Rationale: 1/8 + 1/24
= 1/6
6 * 2
= 12
Answer:B
Answer: (B) 12
Question: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 6.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
(A)  16.5%
(B)  14%
(C)  35%
(D)  55%
(E)  65%
Rationale: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);
On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.065*fringe benefit costs;
So, 35(S+F) = 30S+65F --> S = 6F --> F/S = 1/6 --> F/(S+F) = 1/(1+6) = 1/7 = 0.14.
Answer: B.
Answer: (B)  14%
Question: Mr. Das decided to walk down the escalator of a mall. He found that if he walks down 26 steps, he requires 30seconds to reach the bottom. However, if he steps down 34 stair she would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way insteps?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: here when he step down 26 steps he has 30 seconds for remaining steps.
if he step down 34 stairs he has only 18 sec.
30-18=12
12 secs for 8 steps..
18 secs for 12 steps.
12+34=46
so ans is 46..
ANSWER:B
Answer: (B) 6
Question: Find the fourth proportional to 2.4, 4.6 and 7.6?
(A) 14
(B) 14.657
(C) 15.56
(D) 14.56
(E) None of these
Rationale: Explanation:
Formula = Fourth propotional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56
Answer: Option D
Answer: (D) 14.56
Question: The sum of first five prime numbers is?
(A) 20
(B) 25
(C) 26
(D) 28
(E) 31
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself
Option D
Answer: (D) 28
Question: The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 83, and the average of the female students’ grades was 92, how many female students took the test?
(A) 8
(B) 9
(C) 10
(D) 21
(E) 28
Rationale: Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f
Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 83 Thus M = 664 ---------2
Also, F/f = 92 thus F = 92 F - --------3
Put 2 and 3 in 1: we get
(664+92f)/(8+f) = 90
solving this we get f = 28
Ans: E
Answer: (E) 28
Question: If 6 cats can kill 6 rats in 6 minutes, how long will it take 100 cats to kill 100 rats?
(A) 1 minutes
(B) 2 minutes
(C) 3 minutes
(D) 4 minutes
(E) 6 minutes
Rationale: It will take 6 minutes for 100 cats to kill 100 rats.
1 cat can kill 1 rat in 6 minutes, so 100 cats can kill 100 rats in 6 minutes
Answer E
Answer: (E) 6 minutes
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,400 nuts and 1,400 bolts?
(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,100 seconds
(E) 3,000 seconds
Rationale: I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.
Please can you help how to approach using algebra?
I wouldn't complicate:
1 machine needs 1,400*1 seconds to produce 1,400 bolts, so 2 need half of that, so 1,400/2 seconds.=700
1 machine needs 1,400*2 seconds to produce 1,400 nuts, so 2 need half of that, so 1,400*2/2 seconds.=1400
total = 2100 sec
D
Answer: (D) 2,100 seconds
Question: L.C.M of two prime numbers x and y (x>y) is 161. The value of 3y-x is :
(A) -2
(B) -1
(C) 1
(D) 2
(E) 0
Rationale: Explanation:
H. C. F of two prime numbers is 1. Product of numbers = 1 x 161 = 161.
Let the numbers be a and b . Then , ab= 161.
Now, co-primes with product 161 are (1, 161) and (7, 23).
Since x and y are prime numbers and x >y , we have x=23 and y=7.
inline fn_jvn therefore 3y-x = (3 x 7)-23 = -2 . Answer: A
Answer: (A) -2
Question: A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 1 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
(A) 0.5< t < 0.75
(B) 1.75< t < 2.0
(C) 6.0 < t < 6.5
(D) 2.5 < t < 3.0
(E) 3 < t < 3.5
Rationale: D=2, and R=1
circumference thus is 2pi miles
we know that she walked 1mph
knowing the formula rt=D, we can deduce that t= D/r
D is 2pi miles and r is 1mph
t = 2pi/1
pi can be rewritten as 22/7
2*22/7 = 44/7 and multiply this by 1/1 = 44/7. This is greater than 6, but less than 6.5, therefore, 6<t<6.5. Answer choice C.
Answer: (C) 6.0 < t < 6.5
Question: In how many ways can 4 men and 3 women can arrange with a condition that each men should not sit together and they must be in the order of their age.
(A) 210
(B) 5040
(C) 120
(D) 110
(E) none of these
Rationale: 4 men can take 4 position which can be done in 4!
and women can be sit in 3! ways so 4!*3!
ANSWER:E
Answer: (E) none of these