mathewhe/aqua_rat huggingface dataset:
Question: A bookseller has two display windows. She plans to display 2 new fiction books in the left window, and 5 new non-fiction books in the right window. Assuming she can put the five fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
(A) 240
(B) 72
(C) 144
(D) 336
(E) 420
Rationale: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,
2!*5! =2*120=240
Answer is A
Answer: (A) 240
Question: 12,33,66,88,110,121 which number is wrong in series
(A) 12
(B) 33
(C) 66
(D) 88
(E) 110
Rationale: 12...........
all are multiples of 11 expect 12
ANSWER:A
Answer: (A) 12
Question: In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
(A) 2/9
(B) 2/2
(C) 2/5
(D) 2/6
(E) 2/4
Rationale: Explanation:
A = 2B => B = 1/2 A, so, AB = 2/25
1/2 A2 = 2/25
A2 = 4/25
A = 2/5
Answer:C
Answer: (C) 2/5
Question: At a local appliance manufacturing facility, the workers received a 20% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
(A) 83%
(B) 80%
(C) 20%
(D) 17%
(E) 12%
Rationale: Let's say he works usually 10 hours and earns 100 per hour.
10 * 100 = 1000
10 * 120 = 1200 (this are the new earnings after the raise)
To figure out how much he needs to work with the new salary in order to earn the original 1000:
1000/120 = 8.3333
So he can reduce his work by 1.6666 hours. Which is >15%.
Answer D.
Answer: (D) 17%
Question: John can type a set of pages in 5 hours at a constant rate. If John types for 3 hours and Jack does the rest of the job, who works at 2/5 constant rate of John. How long will it take for Jack alone to do the rest of the job?
(A) 1hrs
(B) 3hrs
(C) 4hrs
(D) 5hrs
(E) 7hrs
Rationale: John will do 3/5 in 3 hrs, so John does 3/5 of the work ..
Therefore, Jack will do the remaining 2/5 th work alone..
As the speed of Jack is 2/5 rate of John, Jack will do the 2/5th work in same time that John takes to complete full job...
ans 5
D
Answer: (D) 5hrs
Question: If the numbers 1 to 96 are written on 96 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
(A) 1/50
(B) 1/25
(C) 1/96
(D) 1
(E) 2
Rationale: There are 25 primes, 70 composite numbers from 1 to 96. The number
which is neither prime nor composite is 1.
Therefore, required probability = 1/96.
ANSWER:C
Answer: (C) 1/96
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 21 revolutions, what will be the number of revolutions made by the larger wheel?
(A) 15
(B) 12
(C) 21
(D) 9
(E) 13
Rationale: Explanation :
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
Cogs6:14}::x:21
⇒6×21=14×x⇒6×3=2×x⇒3×3=x⇒x=9. Answer : Option D
Answer: (D) 9
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat weavers in 8 days ?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Explanation:
Please always remember, that what exactly we need to calculate before applying chain formula. As in this question we need to find how many mats, RIGHT !
So we will compare everything with "number of mats"
As,
More men, More number of mats (Direct Proportion)
More days, More number of mats (Direct Proportion)
So, it can be solved as,
[Weavers 4 4
Days 8 8]::4:x
=>x∗4∗4=8∗8∗4
=>x=16
Option C
Answer: (C) 16
Question: P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?
(A) 6
(B) 8
(C) 7
(D) 4
(E) 1
Rationale: Explanation :
Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6
ANSWER:A
Answer: (A) 6
Question: How many positive integers less than 100 are neither multiples of 3 or 5.
(A) a)30
(B) b)31
(C) c)32
(D) d)53
(E) e)34
Rationale: To answer this Q we require to know
1) multiples of 5 till 100 = 100/5 = 20
2) Multiples of 3 till 100 = 100/3 = 33.33= 33
add the two 20+33=53 ; subtract common terms that are multiple of both 5 and 3..
LCM of 5 and 3 = 15
Multiples of 15 till 100 = 100/15 = 6
so total multiples of 5 and 3 = 53-6 = 47
ans = 100-47 = 53
D
Answer: (D) d)53
Question: Machine A and machine B are each used to manufacture 330 sprockets. It takes machine A 10 hours longer to produce 330 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?
(A) 3.3
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: time taken by B = t
time taken by A = t+10
qty produced by A = q
qty produced by B = 1.1 q
for B: t(1.1q) =330
qt=300
for A: (t+10)(q) = 330
qt+10q=330
300+10q=330
q=3
so A can produce 3/hour.
then B can produce = 3(1.1)=3.3/hour.
A
Answer: (A) 3.3
Question: When an array of pointers is passed through a function, what actually is passed?
(A) number of eleme22
(B) number of elements
(C) first element
(D) last element
(E) address of the starting element
Rationale: Explanation:
When any array is passed through a function,always the address of starting element is passed
Answer: E
Answer: (E) address of the starting element
Question: On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: (C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)
C.P. of 12 balls = S.P. of 17 balls = Rs.720.
C.P. of 1 ball = Rs.720/12= Rs. 60.
answer :E
Answer: (E) 60
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3740. What is the difference between Rose ’s and Tom ’s share in the profit?
(A) s.340
(B) s.362
(C) s.370
(D) s.382
(E) s.390
Rationale: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 3740 × 1/11 = Rs.340.
A)
Answer: (A) s.340
Question: The duplicate ratio of 2:6 is?
(A) 1:2
(B) 1:4
(C) 1:9
(D) 1:18
(E) 1:13
Rationale: 2^2: 6^2 = 4:36=1:9
ANSWER:C
Answer: (C) 1:9
Question: A student appeared in the Mock CAT. The test paper contained 3 sections namely QA, DI and VA. The percentage marks in all VA was equal to the average of percentage marks in all the 3 sections. Coincidentally, if we reverse the digit of the percentage marks of QA we get the percentage marks of DI. The percentage marks in VA scored by student could be:
(A) 81
(B) 48
(C) 66
(D) 69
(E) None of these
Rationale: Solution: Let the percentage marks in QA =(10a +b)%
Let the percentage marks in DI = (10b +a)%
Let the percentage marks in VA = x%.
Now, according to the question, we have,
[(10a+b) + x + (10b+a)] /3 = x
→11a + 11b + x = 3x.
or, x = 11(a +b) /2.
Clearly, we can see that the percentage of the VA section will be a multiple of 11.
So, required answer will be 66.
Answer: Option C
Answer: (C) 66
Question: A man two flats for $675958 each. On one he gains 11% while on the other he loses 11%. How much does he gain or lose in the whole transaction?
(A) 1.21%
(B) 2.56%
(C) 3.12%
(D) 4.65%
(E) 5.12%
Rationale: In such a case there is always a loss
Loss% = (11/10)^2 = 23/19= 1.21%
Answer is A
Answer: (A) 1.21%
Question: Pipes A and B can fill a cistern in 6 and 30 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
(A) 13
(B) 10
(C) 16
(D) 18
(E) 19
Rationale: :
1/6 + 1/30 = 1/5
5 * 2 = 10.Answer:B
Answer: (B) 10
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 7 cm
(B) 6 cm
(C) 5 cm
(D) 1 cm
(E) 9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer: E
Answer: (E) 9 cm
Question: T, U, V are 3 friends digging groups in fields. If T & U can complete i groove in 4 days &, U & V can complete 1 groove in 3 days & V & T can complete in 2 days. Find how many days each takes to complete 1 groove individually
(A) 24/7 days
(B) 23/7 days
(C) 22/7 days
(D) 26/7 days
(E) 14/7 days
Rationale: t+u=1/4, u+v=1/3, v+t=1/2
so 2(t+u+v)=1/4+1/3+1/2=3+4+6/12=13/12.
so (t+u+v)= 13/24.
so t = 13/24-1/3 = 13-8/24= 5/24.,
So T takes 24/5 days to complete the work
Similarly, u takes 24 days and v takes 24/7 days
ANSWER:A
Answer: (A) 24/7 days
Question: If a is a positive integer, then 2^a + 2^(a - 1) =
(A) 2^a
(B) 2^(a + 1)
(C) -1*(2^a)
(D) 2a^(a + 1)
(E) 3(2^a)
Rationale: If a is a positive integer, then 2^a + 2^(a - 1) =
2^a + 2^(a - 1)
2^a(1-2)
-1*(2^a)
Option C is answer
Answer: (C) -1*(2^a)
Question: Distances from you to Man united is written below.
CHELSEA and ARSENAL are 700 kms away
SPURS 1800 kms away
WOLVES 200 kms away
Based on the system , How far should it be to MANCITY ?
(A) 2200 miles.
(B) 2300 miles.
(C) 1900 miles.
(D) 2500 miles.
(E) 2100 miles.
Rationale: E
2100 miles.
Each vowel equivalent to 500 and each consonant equivalent to -200
Answer: (E) 2100 miles.
Question: By selling 32 pencils for a rupee a man loses 60%. How many for a rupee should he sell in order to gain 60%?
(A) 10
(B) 9
(C) 8
(D) 6
(E) 4
Rationale: 40% --- 40
160% --- ?
40/160 * 40 = 10
Answer: A
Answer: (A) 10
Question: A can give B 90 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 120.88
(B) 120.13
(C) 111.22
(D) 120.0
(E) 111.12
Rationale: A runs 1000 m while B runs 910 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/910 = 879.12 m.
B can give C = 1000 - 879.12
=120.88m.
Answer:A
Answer: (A) 120.88
Question: Find the unknown term 8,8,6,X,-4, -12
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: 8,8,6,X,-4, -12
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
2 - 6 = -4
-4 - 8 = -12
ANSWER:A
Answer: (A) 2
Question: By how much is three-fifth of 370 greater than four-seventh of 210 ?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 102
Rationale: Explanation:
3/5 of 370 - 4/7 of 210 = 222 - 120 = 102.
Answer: E
Answer: (E) 102
Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
(A) 15
(B) 16
(C) 18
(D) 25
(E) 20
Rationale: Explanation:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
(20-x / x	x 100 = 25)
=2000 - 100x = 25x
125x = 2000
=x = 16.
ANSWER IS B
Answer: (B) 16
Question: The sum of ages of 5 children born 3 years different each is 50 yrs. What is the age of the Elder child?
(A) 8
(B) 10
(C) 16
(D) 18
(E) 22
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
x+12= 4+12= 16
C
Answer: (C) 16
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
(A) 22
(B) 88
(C) 77
(D) 20
(E) 99
Rationale: In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.
stoppage time = 20/60 hrs = 20 min.
Answer: D
Answer: (D) 20
Question: A child want to buy 3 new toys. If there are 10 toys that satisfy the child's criteria,in how many different ways can the child select the 3 new toys if the order of selection doesn't matter.
(A) 20
(B) 120
(C) 210
(D) 15
(E) 45
Rationale: The number of ways of choosing 3 toys out of 10 are counted by = 10C3 ways = 120
Answer: Option B
Answer: (B) 120
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked atrandom, what is the probability that both are red?
(A) 2/13
(B) 1/14
(C) 5/26
(D) 3/31
(E) 1/17
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: The average of 11 numbers is 10.8. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 9
(B) 9.2
(C) 10
(D) 11.5
(E) 12.6
Rationale: Explanation:
1 to 11 = 11 * 10.8 = 118.8
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 118.8 = 12.6
6th number = 12.6
E)
Answer: (E) 12.6
Question: Helen went to the stationers and bought things worth Euro 30, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Euro 15
(B) Euro 15.7
(C) Euro 19.7
(D) Euro 24.7
(E) None
Rationale: Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [30 - (5 + 0.30)] = Euro 24.70
Answer: Option D
Answer: (D) Euro 24.7
Question: 22 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: in case of cycle no of handshakes = no of persons
hence ans = 22
ANSWER:D
Answer: (D) 22
Question: Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 3 days. In what time Suma can do it alone?
(A) 6
(B) 12
(C) 14
(D) 15
(E) 17
Rationale: Renuâ€™s one dayâ€™s work = 1/6
Sumaâ€™s one dayâ€™s work = 1/3 - 1/6 = 1/6
Suma can do it alone in 6 days.
ANSWER:A
Answer: (A) 6
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 20
(B) 99
(C) 88
(D) 77
(E) 54
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer: A
Answer: (A) 20
Question: In a race of 200 m. A can beat B by 15 m and C by 19 m then how much time C would take To beat B in the race of 3700 m ?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: In 200 race A:B=200/185 , A:C=200/181
than in 3700m race B beats by C,3700- (181/185)*3700=80
ANSWER:D
Answer: (D) 80
Question: If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a^3+b is always even number. 2. ab is even number 3. (a + b) is always an odd number.
(A) II only
(B) III only
(C) I only
(D) I,II only
(E) II,III only
Rationale: 2^3+3 =8+3 = 11 Option I false
odd*even = even. Option II is true
odd + even = odd. Option III is true
Answer : C
Answer: (C) I only
Question: Three numbers are such that the second is as much
lesser than the third as the first is lesser than
the second. If the product of the two smaller numbers
is 85 and the product of two larger numbers is 115.
Find the middle number?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Let the three numbers be x,y,z
2y = x+z.....................1
Given that the product of two smaller numbers is 85
x y = 85................2
Given that the product of two larger numbers is 115
y z = 115...............3
Dividing 2 and 3 x y /y z = 85/115
x / z = 17 / 23
From 1
2y = x+z
2y = 85/y + 115/y
2y2 = 200
y2 = 100
y = 10
ANSWER: A 10
Answer: (A) 10
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) 4029
(B) 4089
(C) 4029
(D) 4096
(E) 1921
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17
= Rs. 4096.
Answer: D
Answer: (D) 4096
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 2
(B) 3
(C) 4
(D) 1
(E) 8
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
ANSWER C
Answer: (C) 4
Question: A store’s selling price of $2500 for a certain printer would yield a profit of 40 percent of the store’s cost for the printer. What selling price would yield a profit of 50 percent of the printer’s cost?
(A) 	$2400
(B) 	$2464
(C) 	$2650
(D) 	$2478
(E) 	$2800
Rationale: 1.4x = 2500
x=2500/1.4
so, 1.5X = 2500*1.5/1.4= 2478
Answer:- D
Answer: (D) 	$2478
Question: A man buys an article for $100. and sells it for $115. Find the gain percent?
(A) 10%
(B) 15%
(C) 25%
(D) 20%
(E) 30%
Rationale: C.P. = $100
S.P. = $115
Gain = $15
Gain% = 15/100 *100 = 25%
Answer is B
Answer: (B) 15%
Question: A reward of $1400 was divided among a group of 36 rescue workers such that each male in the group received $50. How much did each of the 16 females receive?
(A) $10
(B) $12.50
(C) $25
(D) $37.50
(E) $50
Rationale: x = amount each female received
amount each male received = 50
number of females = 16
number of males = 36 - 16 = 20
total to males = 20(50) = 1000
total to females = 16x
reward = total to males + total to females
1400 = 1000 + 16x
1400 - 1000 = 16x
400 = 16x
25 = x
Answer: C
Answer: (C) $25
Question: A train passes a station platform in 62 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 615 m
(B) 240 m
(C) 168 m
(D) 444 m
(E) 691 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/62 = 15 => x
= 444 m
Answer: D
Answer: (D) 444 m
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 4 years?
(A) 14300
(B) 20736
(C) 14500
(D) 14600
(E) 15400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100^4 = 20736
B)
Answer: (B) 20736
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 35%. At what price should he sell the article so as to make a loss of 25%?
(A) s.416
(B) s.480
(C) s.429
(D) s.128
(E) s.419
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 35% = 35% of 640 = Rs.224
SP = CP - Loss = 640 - 224
= Rs.416
Answer:A
Answer: (A) s.416
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
(A) 10.2%
(B) 16.66%
(C) 18.7%
(D) 19.24%
(E) 20%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: (B) 16.66%
Question: Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 2 screws and 4 nails?
(A) a. 4
(B) b. 5/2
(C) c. 2
(D) d. 3/2
(E) e. 5/4
Rationale: let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 2s and 4n= 2s+4*2s=10s..
ratio= 15s/10s=15/10=3/2
D
Answer: (D) d. 3/2
Question: A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Explanation:
Let the side of the square(ABCD) be x meters.
Then, AB + BC = 2x metres.
AC = √2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = 0.59x/2x × 100 % =30% (approx)
Answer: A
Answer: (A) 30
Question: Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
(A) 2 <= 335x+4 <= 6
(B) 2 <= 32x+4 <= 6
(C) 2 <= 334x+4 <= 6
(D) 2 <= 3x+4 <= 6
(E) 2 <= 3466x+4 <= 6
Rationale: The key words in the stem are:a singleline segment offinite length
Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.
Answer: D.
Answer: (D) 2 <= 3x+4 <= 6
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) Rs.1000
(B) Rs.1100
(C) Rs.1050
(D) Rs.1200
(E) Rs.1250
Rationale: Explanation:
1120 = P [1 + (5*12/5)/100]
P= 1000
ANSWER IS A
Answer: (A) Rs.1000
Question: The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 150 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 25 kmph
(B) 17 kmph
(C) 19 kmph
(D) 17 kmph
(E) 29 kmph
Rationale: Speed of the boat in still water
= (100+150)/2
= 125kmph. Speed of the stream
= (150-100)/2
=25 kmph.
Answer: A
Answer: (A) 25 kmph
Question: A car traveled 75% of the way from town A to town B at an average speed of 90 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 37.5
Rationale: Total distance = 100 miles (easier to work with %)
75% of the distance = 75 miles
25% of the distance = 25 miles
1st part of the trip → 75/90 = 0.833
2nd part of the trip → 25/S = t
Total trip → (75+25)/40 = 0.833+ t » 100/40 = 0.833 + t » 2.5 = 0.833+ t » t = 1.667
Back to 2nd part of the trip formula: 25/S = 1.667 » S = 15
Ans A
Answer: (A) 15
Question: Find the least number which when divided by 31 and 9 leaves a remainder of 3 in each case.
(A) 280
(B) 282
(C) 284
(D) 286
(E) 288
Rationale: The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(31, 9) + 3 = 282.
ANSWER:B
Answer: (B) 282
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 T 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 T= 1000+600-25 = 1575
Answer: option C
Answer: (C) 1575
Question: The ratio between the present ages of A and B is 4:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 3:4
(B) 3:0
(C) 3:1
(D) 3:2
(E) 9:5
Rationale: Let the present ages of A and B be 4x and 3x years respectively.
Then, (4x - 4)/(3x + 4) = 1/1
1x = 8 => x = 8
Required ratio = (4x + 4):(3x - 4) = 36:20 = 9:5.Answer: E
Answer: (E) 9:5
Question: Vincent has $12,731 dollars in his wallet. What is the least amount of money (in whole number of dollars) that he must add if he wants to split this money evenly among his nine friends?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 12,731= 14 and 18 is divisible by 9.
Hence we need to add 4 to this number for it to be divisible by 9
Correct Option: D
Answer: (D) $4
Question: For every positive odd integer n, the function h(n) is defined to be the product of all the odd integers from 3 to n, inclusive. If p is the smallest prime factor of h(200) +3, then p is?
(A) between 3 and 20
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) 3
Rationale: h(200) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 200. So h(200)+3 will have 3 in the units digit so smallest prime factor is 3.
Answer: E
Answer: (E) 3
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 27
(B) 22
(C) 20
(D) 87
(E) 23
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km
Answer: C
Answer: (C) 20