divelab/Sys2Bench huggingface dataset:
Question: If the sum of three consecutive even numbers is 30 more than the average of these numbers, then the largest of these numbers is?
Options:
A)20
B)19
C)18
D)17
E)16
Rationale: Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 30
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 90
9x + 18 = 3x + 96
6x = 78
x = 13
Therefore, the largest number is 17.
ANSWER D
Answer: D
Question: If a coin is tossed three times, what is the probability that on the first toss the coin lands tails, on the second toss the coin lands tails, and on the third toss the coin lands heads.
Options:
A)1/2
B)1/8
C)1/6
D)1/4
E)3/8
Rationale: Since there are two options for how a coin can land (heads or tails), that means there is a 1/2 chance to land on tails and a 1/2 chance to land heads. To solve this problem you multiply each probability for each flip together. (1/2) chance to land tails the first time * (1/2) chance to land tails the second time * (1/2) chance to land heads the third time = (1/8) chance to land tails the first two times and heads the third time.
Answer: B
Answer: B
Question: Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 6 hours?
Options:
A) 42
B) 56
C) 84
D) 98
E) 140
Rationale: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 14 mph then the maximum distance, in miles, that the cyclist could travel in 6 hours would be 6*14=98 miles.
Answer: C.
Answer: C
Question: If a dozen of oranges cost $5, what would be the cost of 10 oranges?
Options:
A)3.56
B)4.16
C)4.86
D)5.1
E)5.2
Rationale: The cost of one orange=5/12=0.416
The cost of ten oranges= 0.416x10= $ 4.16
Answer: B
Answer: B
Question: If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible?
Options:
A)10
B)16
C)18
D)12
E)18
Rationale: We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=3!*2!=12 ways
Answer D
Answer: D
Question: On a certain farm the ratio of horses to cows is 3:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 5:3. After the transaction, how many more horses than cows would the farm own?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Originally, there were 3k horses and k cows.
3(3k-15) = 5(k+15)
9k-5k = 75+45
4k = 120
k = 30
The difference between horses and cows is (3k-15)-(k+15) = 2k-30 = 30
The answer is B.
Answer: B
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 39 women together do the work?
Options:
A)10 days
B)30 days
C)20 days
D)80 days
E)40 days
Rationale: C
20 days
Given that 12m = 20w => 3m = 5w
9 men + 39 women = 15 women + 39 women = 54 women
20 women can do the work in 54 days. So, 54 women can do it in (20 * 54) /54 = 20 days.
Answer: C
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)73
B)20
C)83
D)21
E)52
Rationale: Explanation:
1: 2/5 = 5: 2
2/7 * 70 = 20
Answer: Option B
Answer: B
Question: A tap can fill a tank in 12 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)13 hrs 30 mins
B)14 hrs 30 mins
C)15 hrs 30 mins
D)16 hrs 30 mins
E)17 hrs 30 mins
Rationale: Time taken by one tap to fill the tank = 6 hrs.
Part filled by the taps in 1 hour = 4 * 1/12 = 1/3
Remaining part = 1 - 1/2 = 1/2
1/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3 = 1.5 hrs = 1 hrs 30 min
So, total time taken = 13 hrs 30 mins
ANSWER: A
Answer: A
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)18 seconds
B)27 seconds
C)26 seconds
D)12 seconds
E)16 seconds
Rationale: Speed of the boat downstream = 15 + 3
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer:D
Answer: D
Question: The average age of three boys is 24 years and their ages are in proportion 2:4:8. What is the age in years of the youngest boy?
Options:
A)16
B)9
C)18
D)12
E)14
Rationale: 2x + 4x + 6x = 72
x =6
2x = 12
Answer: D
Answer: D
Question: What ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.19.50 ?
Options:
A)10 : 7
B)9 : 8
C)11 : 7
D)13 : 11
E)14 : 8
Rationale: Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 5.50 : 3.50 = 11 : 7
Answer: C
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options:
A)12:15:15
B)12:15:16
C)12:15:19
D)12:45:15
E)12:15:11
Rationale: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B
Answer: B
Question: A man on tour travels first 160km at 64km/hr and the next 160km at 80km/hr. The average speed for the first 320km of the tour is?
Options:
A)56.45km/hr
B)71.11km/hr
C)68.78km/hr
D)75.63km/hr
E)66.56km/hr
Rationale: Total time taken = 160/64 + 160/8 = 9/2 hrs
Average speed = 320*2/9 = 71.11km/hr
Answer is B
Answer: B
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 5 hours?
Options:
A)60X/Y.
B)300X/Y.
C)60Y/X.
D)120Y/X.
E)(X + Y)/60.
Rationale: Kramer can pack X boxes per min.
Therefore in 5 hrs(300mins)he can pack 300X boxes.
If there are Y boxes in one case then then the total number of cases packed by Kramer = 300X/Y
(ANSWER B)
Answer: B
Question: The volumes of two cones are in the ratio 1 : 35 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)7:5
B)2:9
C)7:2
D)2:2
E)2:8
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/35 = (1)2h1/(2)2h2
=> h1/h2 = 7/5
i.e. h1 : h2 = 7:5
Answer: A
Answer: A
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 20 more blue balls than white balls, and thrice as many red balls as blue balls, how many white balls does The box has ?
Options:
A)4
B)10
C)12
D)14
E)16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 20 more blue balls than white balls...
Equation #2: y = 20 + z
...thrice as many red balls as blue balls...
Equation #3: x = 3y
Solve equation #2 for z: z = y - 20
Now, we can replace both x and z with y in Equation #1
3y + y + (y - 20) = 100
5y - 20 = 100
5y = 120
y = 24
There are 24 blue balls. This is 20 more than the number of white balls, so z = 4. That's the answer. Just as a check, x = 72, and 72 + 24 + 4 = 100.
Answer = 4,(A)
Answer: A
Question: How many four-digit numbers that do not contain the digits 3 or 6 are there?
Options:
A)2401
B)3584
C)4096
D)5040
E)7200
Rationale: 1st Digit can be filled up by the numbers - { 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 7 ways
2nd Digit can be filled up by the numbers - { 0, 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways
3rd Digit can be filled up by the numbers - { 0, 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways
So, total No of ways is 7 * 8 * 8 => 3584
Hence answer will be (B)
Answer: B
Question: The H.C.F. of two numbers is 60 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
Options:
A)276
B)300
C)500
D)700
E)900
Rationale: the numbers are (60 x 11) and (60 x 15).
Larger number = (60 x 15) = 900.
ANSWER :E
Answer: E
Question: If 8/ |x| <0, which of the following must be true?
Options:
A)x>8
B)x<8
C)x=8
D)x=4
E)x=0
Rationale: if x<8
then x=6, 8/6>0
if x=8
then 8/8=1
if ifx > 8
for example
x=9 then 8/9<0
ANSWER A x>8
Answer: A
Question: A certain elevator has a safe weight limit of 2,500 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 150 pounds and the average weight of the others being 160 pounds?
Options:
A)7
B)8
C)9
D)10
E)16
Rationale: Lets assume there are 2X people.
Half of them have average weight of 150 and other half has 160.
Maximum Weight is = 2500
So 150*X + 160*X = 2500
=> 310X = 2500
=> X is approximately equal to 8.
So total people is 2*8 = 16
Answer E.
Answer: E
Question: The least common multiple of positive integer e and 3-digit integer n is 690. If n is not divisible by 3 and e is not divisible by 2, what is the value of n?
Options:
A)115
B)230
C)460
D)575
E)690
Rationale: The LCM of n and e is 690 = 2*3*5*23.
e is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to e.
From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.
Answer: B.
Answer: B
Question: Average of five numbers is 20, and the sum of three of the numbers is 48, what is the average of the other 2 numbers?
Options:
A)24
B)34
C)29
D)35
E)26
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=20a+b+c=48(48+d+e)/5=2048+d+e=100d+e=52average=52/2=26Ans E
Answer: E
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 4?
Options:
A)-1
B)0
C)5
D)2
E)3
Rationale: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 4
= x2(x - 2)2 + 4
= (1 + √2)2(1 + √2 - 2)2 + 4
=(√2 + 1)2 (√2 - 1)2 + 4
=[(√2)2 - (1)2]2 + 4
=(2 - 1)2 =1 + 4=5
Correct Option: C
Answer: C
Question: In a camp, there is a meal for 140 men or 240 children. If 180 children have taken the meal, how many men will be catered to with remaining meal?
Options:
A)20
B)35
C)50
D)10
E)40
Rationale: There is a meal for 240 children. 180 children have taken the meal.
Remaining meal is to be catered to 60 children.
Now, 240 children 140 men.
60 children (140/240)	* 60 = 35 men
Answer is B.
Answer: B
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB > YD
B)XB < YD
C)AX > XB
D)CY < YD
E)AX > AB
Rationale: A--X------B
C------Y--D
XB > YD.
Answer: A.
Answer: A
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 5 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 5 minute mark.)
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: 5 minutes is 300 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
300/24=12 plus remainder.
In the time period, Lamp A and Lamp B will flash together 12 times.
Lamp A and Lamp C will flash together every 30 seconds.
300/30=10.
In the time period, Lamp A and Lamp C will flash together 10 times.
Lamp B and Lamp C will flash together every 40 seconds.
300/40=7 plus remainder.
In the time period, Lamp B and Lamp C will flash together 7 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
300/120=2 plus remainder.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 12+10+7-6=23 times.
The answer is C.
Answer: C
Question: If p#q denotes the least common multiple of p and q, then W=((12#16)#(18#24)) = ?
Options:
A) 216
B) 180
C) 144
D) 108
E) 72
Rationale: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB
The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4 = 48.
The greatest common factor of 18 and 24 is 6. So, 18#24 = 18*24/6 = 72
Finally, the greatest common factor of 48 and 72 is 24. So, W=((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72 = 144
The correct answer is C.
Answer: C
Question: A student committee on academic integrity has 42 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: xC1 * (x-1)C1=42
x^2 -x -42 =0
(X-7 (X+6) = 0
X= 7 , -6
-6 can't possible.
Hence 7 should be the answer
A
Answer: A
Question: 0.35 represents what percent of 70?
Options:
A)0.05%
B)0.5%
C)5%
D)500%
E)5000%
Rationale: One more method
0.35 represents what percent of 70?
Divide by 70
0.005 represents what percent of 1?
Answer = 0.005*100 = 0.5% = B
Answer: B
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length
Options:
A)12.9 sec
B)12.1 sec
C)13.9 sec
D)29.9 sec
E)14.9 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Answer: B
Question: At what time between 3 and 4 o’clock, the hands of a clock coincide?
Options:
A)16 4⁄11 minutes past 3
B)15 5⁄61 minutes past 3
C)15 5⁄60 minutes to 2
D)16 4⁄11 minutes to 4
E)None of these
Rationale: Since, in one hour, two hands of a clock coincide only once, so, there will be value.
Required time T = 2⁄11(H × 30 + A°) minutes past H.
Here H = initial position of hour hand = 3(Since 3 o’clock)
A° = required angle = 0°(Since it coincides)
T = 2⁄11(3 × 30 + 0) minutes past 3
= 164⁄11 minutes past 3
Answer A
Answer: A
Question: For which of the following functions is f(q+b)=f(q)+f(b) for all positive numbers q and b?
Options:
A)a) f(x)=x^2
B)b) f(x)=x+1
C)c) f(x)=root x
D)d) f(x)=2/x
E)e) f(x)= -3x
Rationale: f(q+b)=f(q)+f(b) Its E
Answer: E
Question: An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
Options:
A)484
B)676
C)729
D)900
E)1600
Rationale: 729 = 3^6 so it can not be the square of an even number multiplied by an odd number.
The answer is C.
Answer: C
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)29/98
C)18/37
D)18/29
E)18/29
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35
= 18/35
Answer:A
Answer: A
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years B in which the population would be doubled assuming there is no emigration or immigration is
Options:
A)20
B)25
C)B=30
D)B=35
E)B=40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000=1000(1+(2/100))^n
n=35 Answer is D.
Answer: D
Question: A certain drive-in movie theater has total of 12 rows of parking spaces. There are 10 parking spaces in the first row and 11 parking spaces each in the next two rows. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater?
Options:
A)219
B)221
C)321
D)192
E)202
Rationale: First row 10, Second row 11 and then other 10 rows form an Arithmetic Progression with first term 11 and last term 29 and Avg is 20.
so 20*10+10+11=221
Answer is B
Answer: B
Question: When a certain shoe store reduces the price of its best-selling style of shoe by 20 percent, the weekly sales of this style increase by 20 percent. Which of the following best describes the resulting change in the store's weekly revenue from sales of this style of shoe?
Options:
A)Revenue decreases by 4%
B)Revenue decreases by 1%
C)There is no change in revenue
D)Revenue increases by 1%
E)Revenue increases by 10%
Rationale: Old price = 10, old sales = 10 --> old revenue = 100;
New price = 8, new sales = 12 --> new revenue = 96.
Revenue decreased by 4%.
Answer: A.
Answer: A
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
Options:
A)9688
B)9687
C)9685
D)9682
E)9680
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}2 = Rs.9680
Answer:E
Answer: E
Question: A boy swims downstream 56 km and upstream 42 km taking 7 hours each time; what is the speed of the current?
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: 56 --- 7 DS = 8
? ---- 1
42 ---- 7 US = 6
? ---- 1 S = ?
S = (8 - 6)/2 = 1
Answer:E
Answer: E
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Four years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Options:
A)Can't be determined
B)40
C)27
D)32
E)None of these
Rationale: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+4)/(4x+4)=11/9
⇒ 45x + 36 = 44x + 44⇒ 9(5x +4 ) = 11(4x + 4)
⇒ 45x - 44x = 44 - 36
⇒ x = 8.
Anand's present age = 4x = 32 years.
Answer: D
Answer: D
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.5 per sq m?
Options:
A)675, Rs.3375
B)575, Rs.1350
C)1350, Rs.675
D)1450, Rs.775
E)1550, Rs.875
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 5 = Rs.3375
ANSWER:A
Answer: A
Question: In an exam, Amar scored 84 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
Options:
A)437.33
B)457.33
C)537.33
D)637.33
E)497.33
Rationale: Average mark scored by all the three boys =
[84/100 (800) + 36/100 (800) + 44/100 (800)] / 3 = 437.33
ANSWER:A
Answer: A
Question: Sujal covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 25%.
Options:
A)60 km/h
B)70 km/h
C)75 km/h
D)80 km/h
E)85 km/h
Rationale: Given Speed = 60 Kmph.
It means Sujal covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km.
25% time reduced = 40 - 25% of 40 = 30 min.
Thus, Sujal needs to cover 40 km in 30 min (0.5 hour).
Speed * Time = Distance.
Speed * 0.5 = 40
Speed = 80 kmph.
ANSWER : OPTION D
Answer: D
Question: There are 800 military people in a division of the army. There is one Officer for every 15 soldiers in that division. Now the question is how many officers are in the division?
Options:
A)22
B)32
C)37
D)73
E)75
Rationale: B
32
24 soldiers + 1 officer makes a group of 25 people. Now number of such groups = 800/25 = 32.
Answer: B
Question: Last year a certain bond price with a face value of 5000 yielded 7% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
Options:
A)4063
B)5325
C)5385
D)6000
E)6154
Rationale: Interest = 0.07*5000 = 0.065*selling price --> selling price = 0.07*5000/0.065 --> selling price = ~5,385
Answer: C.
Answer: C
Question: A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 5 more days. How many days would it have taken the second carpenter to do the complete job working alone?
Options:
A)4.5
B)7.5
C)9.5
D)17.5
E)24.5
Rationale: A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 5 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+5*1/x=1
5x+35=7x
2x=35
x=17.5 days.
Ans:D
Answer: D
Question: The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)38 cm2
B)85 cm2
C)65 cm2
D)40 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 32/2 = 40 cm2
Answer:D
Answer: D
Question: The distance from City A to City B is 180 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 120 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
Options:
A)42
B)45
C)46
D)48
E)50
Rationale: The time it takes Cara to drive to City B is 180 / 30 = 6 hours.
Dan needs to take less than 4 hours for the trip.
Dan needs to exceed a constant speed of 180 / 4 = 45 miles per hour.
The answer is B.
Answer: B
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 3 different offices?
Options:
A)64
B)65
C)66
D)67
E)68
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 4*4*4=4^3=64.
Answer: A.
Answer: A
Question: Two years ago, P was half of Q's age. If the ratio of their present ages is 3:4 what will be the total of their present ages?
Options:
A)3
B)7
C)9
D)1
E)5
Rationale: Let present age of P and Q be 3x3x and 4x4x respectively.
Two years ago, P was half of Q's age
â‡’(3xâˆ’2)=1/2(4xâˆ’2)
â‡’6xâˆ’4=4xâˆ’2
â‡’2x=2
â‡’x=1
Total of their present ages
=3x+4x=7x=7Ã—1=7
B
Answer: B
Question: what is the remainder when 4.4!*5.5!*6.6!...........19*19! is divided by 64
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: (4*4*3*2*5*5!*6*5*.......*1*7*7!..........)/64=(int value) no remender there
ANSWER:A
Answer: A
Question: If a, b are integers and |a-b|=6, which of the following is the smallest possible value of ab?
Options:
A)-16
B)0
C)16
D)-9
E)40
Rationale: a=3, b=-3. Hence, the answer is D.
Answer: D
Question: Two pipes P and Q can fill a cistern in 16 and 18minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)11 1/2
B)13 1/2
C)13 1/3
D)13 1/5
E)13
Rationale: 4/16 + x/18 = 1
x= 13 1/2.Answer: B
Answer: B
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
Options:
A)35
B)36
C)37
D)39
E)40
Rationale: Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 7)/(6x + 7) = 6/7
7(5x + 7) = 6(6x + 7) => x = 7
X's present age = 5x = 35 years
ANSWER:A
Answer: A
Question: If the positive integer x is a multiple of 176 and the positive integer 222 is a multiple of 6, then xy must be a multiple of which of the following?
I. 7
II. 44
III. 41
Options:
A)II only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: x=176a
y=222b
xy=39072ab
where a,b are integers
Hence , xy will always be divisible by 8,12 .
A is the answer.
Answer: A
Question: How many times in a day, are the hands of a clock in straight line but opposite in direction?
Options:
A)20
B)22
C)24
D)32
E)48
Rationale: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clock only). So, in a day, the hands point in the opposite directions 22 times.Answer : B
Answer: B
Question: Express a speed of 36 kmph in meters per second?
Options:
A)10
B)22
C)88
D)299
E)22
Rationale: 36 * 5/18 = 10 mps
Answer: A
Answer: A