mathewhe/aqua_rat huggingface dataset:
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio W of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
(A) 8:3
(B) 3:2
(C) 4:3
(D) 2:3
(E) 3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio W of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: (B) 3:2
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.840 find the share of A.
(A) 240
(B) 388
(C) 379
(D) 277
(E) 320
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 840 = 320
Answer: E
Answer: (E) 320
Question: 3x^2-6x+3 = 0
Find the above equation find the value of x
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: (B) 1
Question: If x#y is defined to equal x^2/y for all x and y, then (-1#2)#2 =
(A) 4/3
(B) 1/3
(C) 1/12
(D) 1/8
(E) -4/3
Rationale: (-1)^2 / 2 = 1/2
(1/2)^2 / 2 = 1/8
so D is my answer
Answer: (D) 1/8
Question: A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability Z that the game will end after the fourth throw?
(A) 1/16
(B) 3/32
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: Another approach:
Two likely scenarios would be : HHTH or THTH
for each of the scenarios probability would be 1/16
So Probablilty Z is 1/16 + 1/16 = 1/8.C
Answer: (C) 1/8
Question: A rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) s.3988
(B) s.3900
(C) s.3228
(D) s.3922
(E) s.3600
Rationale: Area = (l + b – d) d
(70 + 60 – 10)10 => 1200 m2
1200 * 3
= Rs.3600
Answer:E
Answer: (E) s.3600
Question: A team of eleven footballers has an average height of 170 cm. Four footballers whose average height is 140 cm, left the team and four new others whose average height is 124 cm, joined. Calculate the new average height of the footballers (in cm) is?
(A) 166.2 cm
(B) 154.2 cm
(C) 364.2 cm
(D) 124.2 cm
(E) 164.2 cm
Rationale: Total height = 170 * 11 = 1870 cm.
Total height of those who left = 140 * 4 = 560
Total height of those who joined = 124 * 4 = 496
New average
= [1870 - 560 + 496 ] / 11 = 1806/11 cm.
= 164.2 cm
Answer:E
Answer: (E) 164.2 cm
Question: A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.
(A) 32 Cm2
(B) 16 Cm2
(C) 20 Cm2
(D) 64 Cm2
(E) None of these
Rationale: Solution: Side of the first square is 4 cm.
side of second square = 2 √2 cm.
Side of third square = 2 cm.
and so on. i.e. 4, 2 √, 2, √2, 1 ......
Thus, area of these square will be,
= 16, 8, 4, 2, 1, 1/2 ....... Hence, Sum of the area of first, second, third square ......
= 16+8+4+2+1+ .....
= [16/{1-(1/2)}] = 32 Cm2.
Answer: Option A
Answer: (A) 32 Cm2
Question: If f(a)=4a-6, what is the value of (f(5a)-f(a))/2 ?
(A) 12a-6
(B) 10a+5
(C) 5a/6
(D) 4a-6
(E) 20a+6
Rationale: f(a)=4a-6
f(5a) = 20a-6
(f(5a)-f(a))/2 = (20a-6+4a-6)/2 = 12a-6
Answer is
Answer: (A) 12a-6
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 229
(B) 238
(C) 500
(D) 288
(E) 211
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.Answer: C
Answer: (C) 500
Question: If the time is currently 1:30pm, what time will it be in exactly 842 hours?
(A) 12:30am
(B) 3:30am
(C) 12:30pm
(D) 2:30pm
(E) 10:30pm
Rationale: Every 24 hours will bring us to the same 1:30pm. 840 is divisible by 24 (35*24=840), so if it were 840 hours we would have 1:30pm, but since it's 842 hours then it will be 2 hour more, so 13:30pm.
Answer: B
Answer: (B) 3:30am
Question: n is a positive integer, and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1440, then the smallest possible value of n is
(A) 8
(B) 12
(C) 16
(D) 18
(E) 24
Rationale: When we say k is the product of all integers from 1 to n, we mean k = n!
Now 1440 = 1.2.3.4.5.6.2
Now if k is a multiple of 1440, it has to be at least 8!. This is so because it cannot be 6! due to the extra 2 factor at the end; it cannot be 7! either, again because the extra 2 in the end will be unaccounted for.
If k = 8! = 1.2.3.4.5.6.7.8, then k = 1440*7*4 i.e. k will be a multiple of 1440.
Answer A
Answer: (A) 8
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 800
(B) 802
(C) 821
(D) 897
(E) 828
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: A
Answer: (A) 800
Question: If the cost price is 75% of the selling price, then what is the profit percent?
(A) 5%
(B) 11%
(C) 13%
(D) 21%
(E) 33%
Rationale: Let S.P. = $100
C.P. = $75
Profit = $25
Profit% = 25/75 * 100 = 25/6 = 33% approximately
Answer is E
Answer: (E) 33%
Question: A small library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
(A) 200
(B) 300
(C) 285
(D) 400
(E) 450
Rationale: avg visitors on sundays = 510
tot visitors of 5 sundays = 510*5
avg visitors of other 25 days = 240*25
tot visitors = (510*5)+(240*25)
tot days = 30
avg no of visitors per day =(510*5)+(240*25)/30
=285
ANSWER C
Answer: (C) 285
Question: The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $30 and other expenses per hous is $ 20, then what would be the minimum expenditure required to cover a distance of 400 Km?
(A) 300
(B) 400
(C) 250
(D) 350
(E) 450
Rationale: 50 kmph consumption is 1 lt/hr
so 400 km will take 8 hrs and the consumption is 8 lt for entire distance.
1 lt costs $30
so 8 lt costs $240
extra expenses for 1 hr - $20
8 hrs - $160
total expense - $240 + $160= $400
Answer : B
Answer: (B) 400
Question: Scott's average (arithmetic mean) golf score on his first four rounds was 68.What score does he need on his fifth round to drop his average score by 2 points?
(A) 58
(B) 72
(C) 78
(D) 88
(E) 312
Rationale: Average score for first 4 rounds = 68
Average score after 5 rounds = 66
Score Scott needs on his 5th round to drop average score by 2 points = 68 - (2*5) = 58
Answer A
Answer: (A) 58
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 2
(B) 5
(C) 8
(D) 7
(E) 3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: (C) 8
Question: How many numbers from 13 to 76 are exactly divisible by 10?
(A) 5
(B) 6
(C) 9
(D) 11
(E) 12
Rationale: Option 'B'
13/10 = 1 and 76/10= 7 ==> 7 - 1= 6 Numbers
Answer: (B) 6
Question: A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,500 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: D for me.
Let managers comminsion rate be M.
m*5000+ 2*0.05*5000=2500
5000*m=2000
m=40/100=40%
Answer: (D) 40%
Question: Three tenths of the wooden toys were painted blue and one fourth of them were painted green.
Half of the remaining toys were painted red and half were painted yellow. If 300 toys are blue, how
many are there of yellow toys?
(A) 132
(B) 246
(C) 321
(D) 225
(E) 437
Rationale: .3 x T = 300 blue toys
T = 300 ÷ .3
T = 1000 toys in all
1/4 x 1000 = 250 green toys
300 + 250 = 550 blue or green toys
1000 - 550 = 450 remaining toys
1/2 x 450 = 225 red toys
1/2 x 450 = 225 yellow toys
correct answer D
Answer: (D) 225
Question: The function f is defined for all positive integers t by the following rule. f(t) is the number of positive integers each of which is less than t and has no positive factor in common with t other than 1. If p is any prime, number then f(p)=
(A) p-2
(B) p-1
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
For example: if p=6 how many numbers are less than 6 having no common factors with 6: 1, 2, 3, 4, 5, --> 6-1=5.
Answer: B.
Answer: (B) p-1
Question: When y is divided by 264, the remainder is 42. What is the remainder when the same y is divided by 22?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: y = 264*a + 42 = (22*12)*a + 22 + 20
The answer is E.
Answer: (E) 20
Question: The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 64, what is the value of x?
(A) 0
(B) 2
(C) 4.8
(D) 4.67
(E) 10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+5)^2A2= (2x-3)^2
L1= x+5L2= 2x-3
P1 = 4( x+5)P2=4(2x-3)
P1+P2=64
4( x+5) +4(2x-3)=64............> X=4.8
Answer: C
Answer: (C) 4.8
Question: A man can row upstream at 12kmph and downstream at 16 kmph. The speed of the stream is
(A) 2 km/hr
(B) 4 km/hr
(C) 5 km/hr
(D) 10 km/hr
(E) None
Rationale: Sol.
Speed of stream = 1/2(16 -12) kmph = 2 kmph.
Answer A
Answer: (A) 2 km/hr
Question: In a class there are 18 boys and 10 girls. In how many ways can a boy and a girl be selected?
(A) 180
(B) 500
(C) 277
(D) 266
(E) 255
Rationale: We can select one boy from 18 boys in 18 ways.
We select one girl from 10 girls in 10 ways
We select a boy and girl in 18 * 10 ways i.e.,
= 180 ways.
Answer: A
Answer: (A) 180
Question: I bought two books; for Rs.420. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 197
(B) 245
(C) 189
(D) 278
(E) 268
Rationale: x*(85/100)
= (420 - x)119/100
x = 245
Answer: B
Answer: (B) 245
Question: The charge for a single room at Hotel P is 20 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
(A) 15%
(B) 20%
(C) 12.5%
(D) 50%
(E) 150%
Rationale: Let rate in R = 100x
then P = 80x
G = 100y
P = 90y
Thus
80 x=90y
or x = 1.125 y
Ans R = 112.5y
so increase = 12.5%
Answer: C
Answer: (C) 12.5%
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 7, and the digit 2 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 300
(E) 320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 7.
Four digit # possible without the restriction (about the digit 2): 4*5*4*2=160
Numbers with two 2-s, 2X2X 1*5*1*2=10.
Thus there are 160-10=150 such numbers.
Answer: B.
Answer: (B) 150
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.063. What is the value of x?
(A) 0.01
(B) 0.02
(C) 0.04
(D) 0.05
(E) 0.055
Rationale: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*35 and brand C=0.08*25
Total number of widgets=40+35+25=100
the probability that the widget selected is defective is 0.063=(x*40+0.06*35+0.08*25)/100
=> 40x+2.1+2=6.3
=>40x=2.2
>x=2.2/40=0.055
Ans E
Answer: (E) 0.055
Question: There are 9 novel books, 4 drama books, 12 poetry books and 7 grammar books in my bookshelf. The books are randomly arranged in the shelf and not at all in the order of their type. What is the least number of books that must be drawn from the shelf in order to get 6 books of a particular type?
(A) 20
(B) 23
(C) 25
(D) 28
(E) None of these
Rationale: If we remove all drama books that is 4 of them are gone out of 20 left with 16.
Now suppose 5 of each novel, poetry and drama are drawn out from the shelf, that is 15 more books gone, so total 19 are taken out from the shelf and left with 1.
Now the next 1 book which is pulled can be any of the three categories but it would definitely complete a set of 6 for one of the them.
1. Take out 4 Dramas.
2. Take 5 of each of the other 3, total of 15.
3. Next book you take will complete a set of 6.
Total is 4+15+1 = 20.
ANSWER:A
Answer: (A) 20
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 4
(B) 6
(C) 2
(D) 3
(E) 8
Rationale: 9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
ANSWER D
Answer: (D) 3
Question: What is the difference between the largest number and the least number written with the digits 6, 3, 2, 5?
(A) 6084
(B) 4176
(C) 2077
(D) 2721
(E) 1812
Rationale: Explanation:
2356
6532
------------
4176
Answer:B
Answer: (B) 4176
Question: Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 16% the new mean is $850.What was original rent of friend whose rent is increased?
(A) 800
(B) 900
(C) 1000
(D) 1100
(E) 1250
Rationale: 0.16X = 4(850-800)
0.16X = 200
X = 1250
Answer E
Answer: (E) 1250
Question: Find the one which does not belong to that group ?
(A) 27
(B) 37
(C) 47
(D) 67
(E) 17
Rationale: Explanation:
37, 47, 67 and 17 are prime numbers but not 27.
ANSWER IS A
Answer: (A) 27
Question: 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
(A) 33
(B) 89
(C) 12
(D) 77
(E) 61
Rationale: 9M + 12B ----- 12 days
12M + 12B ------- 10 days
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days
Answer:C
Answer: (C) 12
Question: If (8x)/(1 - 10y/z) = 3x then which of the following is true?
(A) z = 5y
(B) z = -6y
(C) z = y
(D) z = -y
(E) z = 6y
Rationale: (8x)/(1 - 10y/z) = 3x
=> 8z/(z - 10y) = 3
=> 8z = 3z - 30y
=> 5z = -30y
=> z = -6y
Hence Ans is B
Answer: (B) z = -6y
Question: If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 =
(A) 7
(B) 11
(C) 14
(D) 17
(E) 20
Rationale: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 13-2*3=7..
Answer A
Answer: (A) 7
Question: If A(k)=(k+1)^k, and k=1, what is the value of A(A(A(k-1)))?
(A) 0
(B) 2
(C) 1
(D) 6
(E) 9
Rationale: A(A(A(0)))=A(A(0))=A(0)=1.
Thus, the answer is C.
Answer: (C) 1
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
(A) 360
(B) 580
(C) 720
(D) 5040
(E) None of these
Rationale: Considering vowels as a single entity, we have 5 (distinct) entities... So 5! permutations are there... In each of them, there are 3! different permutations possible (within the vowels)...
So, total arrangements = 5! * 3! = 720
ANSWER:C
Answer: (C) 720
Question: (?) - 19657 - 33994 = 9999
(A) 63641
(B) 63645
(C) 63650
(D) 63652
(E) 63656
Rationale: 19657 Let x - 53651 = 9999
33994 Then, x = 9999 + 53651 = 63650
-----
53651
-----
C
Answer: (C) 63650
Question: A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
(A) 1 km/hr
(B) 2 km/hr
(C) 1.5 km/hr
(D) 2.5 km/hr
(E) 3.5 km/hr
Rationale: Explanation:
Assume that he moves 4 km downstream in
x
x hours
Then, speed downstream
=
distance/time =4/xkm/hr
Hence, speed downstream
=4/x=4/(1/2)=8km/hr
speed upstream = 3/x=3/(1/2)=6km/hr
Hence, rate of the stream =1/2(8-6)=1km/hr
ANSWER IS A
Answer: (A) 1 km/hr
Question: 8 speakers gathered to deliver speeches on two topics. Even though 8 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?
(A) 2
(B) 36
(C) 64
(D) 100
(E) 1024
Rationale: 1)there are 8 speeches in ONE topic and 8 in OTHER..
2)there is a specific order for topics, so
a) both the topics are to be spoken on- so ONE from each
b) the order does not matter since there is ONLY one specific order..
so 8C1∗8C1=8∗8=64
ANSWER:C
Answer: (C) 64
Question: There are 35 students in a hostel. If the no. of students increases by 9, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) 334.44
(B) 340.88
(C) 342.88
(D) 345.88
(E) 380
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 9) = x – 1
or, 35x + 42 = 44x – 44
or, x = 9.55
Thus the original expenditure of the mess = 35 x 9.55 = Rs. 334.44
A
Answer: (A) 334.44
Question: In the xy plane line m has the equation 4x + y = t. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
(A) -4/3
(B) 1/4
(C) -4
(D) 3/4
(E) 4/3
Rationale: The equation of line m is y=-4x+t. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
Answer: (A) -4/3
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7
(D) 82
(E) 43
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
Answer: (A) 5
Question: Three pounds of 05 grass seed contain 5 percent herbicide. A different type of grass seed, 20, which contains 20 percent herbicide, will be mixed with three pounds of 05 grass seed. How much grass seed of type 20 should be added to the three pounds of 05 grass seed so that the mixture contains 10 percent herbicide?
(A) 3
(B) 3.75
(C) 1.5
(D) 6
(E) 9
Rationale: 05 grass seed contains 5% herbicide and its amount is 3 pound
20 grass seed contains 20% herbicide and its amount is x
when these two types of grass seeds are mixed, their average becomes 15%
thus we have
3(5)+x(20)/(x+3) = 10
15+20x=10x +30
10x=15
or x=1.5
C
Answer: (C) 1.5
Question: In order to fulfill a local school’s request for x cakes, B parents agreed to each bake an equal number of cakes. If y of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?
(A) xy
(B) xy/B
(C) yx/(B(B-y))
(D) yx/B-y
(E) 2xy
Rationale: No of cakes each parent has to bake : x/B
No of parents did not bake cake = y
No of cakes that were not baked by p parents = y*x/B
No of parents has to bake additional cakes = B-y
additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = yx/(B(B - y))
Answer C
Answer: (C) yx/(B(B-y))
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 15 pages.
(A) 8
(B) 10
(C) 12
(D) 14
(E) 6
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(15/2.5)=6 hrs
ANSWER:E
Answer: (E) 6
Question: For a positive integer n, if 5^n is a factor of 20!, but 5^n+1 is not a factor of 20!, what is the value of n?
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 20! has four 5's
20/5 = 4
Thus 5^4 can completely divide 20! and 5^5 can not divide 20!
So, Answer will be (A) 4
Answer: (A) 4
Question: A tap can fill a tank in 8 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 5 hr
(B) 1 hr 30 min
(C) 2 hr 30 min
(D) 2 hr
(E) 4 hr
Rationale: Explanation:
A tap can fill a tank in 8 hours.
Therefore the tap can fill half the tank in 4 hours.
Remaining part =1/2
One tap take time to fill half of the tank = 4 hrs
4 taps take time to fill half of the tank = 4/4 hrs = 1 hr
Total time taken to fill the tank = 4+1 hrs = 5 hrs
Answer : A
Answer: (A) 5 hr
Question: A person travels equal distances with speeds of 2km/hr, 6km/hr, 6km/hr. and takes a total time of 11minutes. Find the total distance ?
(A) 1km
(B) 500mts
(C) 660mts
(D) 2km
(E) 250mts
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/2)+(x/6)+(x/6) = 11/60
x=0.22
total distance = 3*0.22 = 0.66km = 660meters
correct option is C
Answer: (C) 660mts
Question: D is the set of all the multiples of 5 between 20 and 100. E is the set of all the factors of 999. Set D and Set E have how many numbers in common?
(A) 2
(B) 1
(C) 3
(D) 0
(E) 12
Rationale: D is a set of multiples of 5.
999 is NOT a multiple of 5, hence none of its factors is a multiple of 5.
Therefore, those two sets won't have any overlap.
Answer: D
Answer: (D) 0
Question: A 3-letter code word consists of letters A, B. If the code includes all the two letters, how many such codes are possible?
(A) 72
(B) 48
(C) 6
(D) 24
(E) 18
Rationale: A-AB can be arranged in 3!/2!=3 ways;
B-AB can be arranged in 3!/2!=3 ways;
Total: 3+3=6.
Answer: C.
Answer: (C) 6
Question: Find the remainder Q when 12^190 is divided by 1729 ?
(A) 12
(B) 1
(C) 1728
(D) 1717
(E) 4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder Q -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: (D) 1717
Question: Rahim bought 4 pillows with the average cost of $5. If Rahim also buys the fifth pillow with the price of $ 10, what is the average (arithmetic mean) price of those 5 pillows?
(A) $6
(B) $5
(C) $5.5
(D) $6.5
(E) $7
Rationale: 4 pillowss -> Total cost = 4 * Avg cost = 4*5 = 20
Fifth pillow cost = 10
Total cost for 5 pillows = 20+10 = 30
AM = 30/5 = 6
Hence A
Answer: (A) $6