mathewhe/aqua_rat huggingface dataset:
Question: A wheel has a diameter of y inches and a second wheel has a diameter of x inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 100xy
(B) 100y - x
(C) 100x - y
(D) 100y/x
(E) 100x/y
Rationale: First Wheel with diameter y inches ----> So the circumference = y*pi --------- (1)
Second Wheel with diameter x inches ----> So the circumference = x*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
100 = d/(y*pi)
d = 100 * y * pi ---------- (3)
From equation (2)
Revolutions = d/(x*pi) = (100 * y * pi) / (x*pi) = 100y/x
Answer (D)
Answer: (D) 100y/x
Question: Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?
(A) 7
(B) 10
(C) 14
(D) 15
(E) 16
Rationale: Explanation: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on.
Answer: Option D
Answer: (D) 15
Question: What is 50% of 40% of 1200 grams?
(A) 450 gms
(B) 100 gms
(C) 300 gms
(D) 240 gms
(E) None of these
Rationale: 50/100 × 40/100 × 1200= 240
Answer: D
Answer: (D) 240 gms
Question: If a > 1, b > 1, and (a^2)b = a, then which of the following MUST be true?
(A) a > b
(B) 2a > b
(C) a^2< b^2
(D) ab > b
(E) a^3 < b^3
Rationale: If b is positive, then we have that a>b>0.
If b is negative, then we have that a<b<0.
A) a > b. Not necessarily true.
B) 2a > b. Not necessarily true.
C) a^2< b^2 then a>b not necessarily true.
D) ab>b If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So,this statement is always true.
E)a^3<b^3= axaxa>bxbxb ,not necessarily true.
Therefore D is correct
Answer: (D) ab > b
Question: A wolf eats 4.5 Kg of meat in 2 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in three days?
(A) 10.
(B) 9.
(C) 8.
(D) 7
(E) 6.
Rationale: We will have to get them to common ratio may be per 4 days and then convert to 3 days...
So wolf will it 5.5*2=11 kgs in 4 days...
Total in 4 days = 11+3=14...
So in 3 days= 14*3/4=10.5...
For answer to be B, wolf could be eating 4.5....
So 4.5*2=9..
Combined 9+3=12 in 4 days..
In three days 12*3/4=9
ANSWER:B
Answer: (B) 9.
Question: 137+276=435 how much is 731+672?
(A) 534
(B) 1403
(C) 1623
(D) 1513
(E) 1613
Rationale: 137-731 and 276-672 similarly 435-534
ANSWER:A
Answer: (A) 534
Question: A man tosses three coins in the air. When they land, he finds that two of the coins have heads up and one has tails up.
What is the probability that when the coins are tossed again, they will land again with two heads up and one tails up.
Please note that the coins are unbiased.
(A) 50%
(B) 40%
(C) 70%
(D) 60%
(E) 55%
Rationale: A
50%
Explanation:
When the coins are tossed there can be eight possible outcomes (2*2*2)
HHH
HTT
HTH
HHT
TTT
THH
THT
TTH
If you find out, we have only four favorable outcomes. Also, the events here are independent and thus we can calculate the probability by using these only.
Thus the probability is 50 percent.
Answer: (A) 50%
Question: Which one of the following numbers is exactly divisible by 11?
(A) 9
(B) 10
(C) 11
(D) 13
(E) 15
Rationale: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
C
Answer: (C) 11
Question: The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people C who purchased only book A?
(A) 250
(B) 500
(C) 750
(D) 1000
(E) 1500
Rationale: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, C=1000 purchased A only. (This is much simpler to solve using the Venn diagram).
Correct answer is D. 1000
Answer: (D) 1000
Question: Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 6:00 am and Pipe B at 7:00 am, at what time will the pool be full?
(A) 14:00
(B) 15:00
(C) 13:00
(D) 16:00
(E) 17:00
Rationale: Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 6:00 a.m and Pipe B at 7:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 7:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12
Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1
Therefore, it takes 10 hrs to fill the pool
As Pipe A started at 6:00 a.m, pool is full at 16:00 hrs
Answer : D
Answer: (D) 16:00
Question: If $792 are divided between worker A and worker B in the ratio 5:6,what is the share that worker B will get?
(A) 54.54%
(B) 55.55%
(C) 56.56%
(D) 57.57%
(E) 58.58%
Rationale: Worker B will get 6/11 = 54.54%
The answer is A.
Answer: (A) 54.54%
Question: If the cost price of 10 pens is equal to the selling price of 8 pens, the gain percent is:
(A) 9%
(B) 25%
(C) 50%
(D) 80%
(E) 34%
Rationale: Solution :
Let cost price of the price be Rs.1
8 pens C.P. = 8
10 pens S.P. = 10
Gain = 2/8*100 = 25 %
Answer : B
Answer: (B) 25%
Question: A cyclist covers a distance of 800 meter in 4 minutes 20 seconds. What is the speed in km/hr of the cyclist?
(A) 6.2 km/h
(B) 8.4 km/hr
(C) 11.05 km/hr
(D) 16.07 km/hr
(E) 15.07 km/hr
Rationale: Speed =	Distance /Time
Hint: Convert minutes into seconds
Time=4 min 20 sec =260 sec
Speed =	800 /260
= 3.07 m/sec
Convert the speed from m/s to km/hr by multiplying with (5/18)
3.07 x	18 /5 km/hr = 11.05 km/hr
ANSWER IS C
Answer: (C) 11.05 km/hr
Question: In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is :
(A) 12
(B) 11
(C) 10
(D) 27
(E) 22
Rationale: Explanation:
Total employees = \inline \frac{(25-10)\times 20}{10}=30
Hence number of educated employees = 30-20 = 10
Answer: C) 10
Answer: (C) 10
Question: Current age of Bruce and Tomy r in the ratio of 5:4 respectively. 3 years hence, the ratio of their ages will become 11:9 respectively. What is Tomy 's present age in years?
(A) 16 years
(B) 20 years
(C) 24 years
(D) 26 years
(E) 28 years
Rationale: Let the present ages of Bruce and Tomy be 5x years and 4x years respectively.
Then, 5x + 3 = 11
4x + 3 9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6.
Anand's present age = 4x = 24 years.
C
Answer: (C) 24 years
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
(A) 2
(B) 2(2/9)
(C) 3 (3/7)
(D) 3 (1/7)
(E) 4
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: (B) 2(2/9)
Question: Square A is inscribed in circle B. If the perimeter of A is 32, what is the circumference of B?
(A) 6√ 2π
(B) 4√ 2π
(C) 8√ 2π
(D) 7√ 2π
(E) 5
Rationale: square forms two right angled triangles.
Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.
hypotenuse here = diagonal of the square = 8 sqrt(2) = diameter
=> radius = 4 sqrt(2)
Circumference of the circle = 2pi r = 8 pi sqrt(2)
Answer is C.
Answer: (C) 8√ 2π
Question: There are 8 executives, including the CEO and CFO, that are asked to form a small team of 4 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
(A) 45
(B) 55
(C) 65
(D) 75
(E) 85
Rationale: The total number of ways to form a team of 4 is 8C4=70.
We need to subtract the number of teams that have both the CEO and the CFO.
The number of teams with both the CEO and CFO is 6C2=15.
The number of ways to form an acceptable team is 70-15=55.
The answer is B.
Answer: (B) 55
Question: 33 1/3% OF 240?
(A) 80
(B) 90
(C) 110
(D) 120
(E) 130
Rationale: 33 1/3 % = 1/3
1/3 × 240 = 80
A)
Answer: (A) 80
Question: If a = 105 and a^3= 21 * 49 * 45 * b, what is the value of b?
(A) 25
(B) 42
(C) 45
(D) 49
(E) 54
Rationale: First step will be to break down all the numbers into their prime factors.
105 = 3 * 5 * 7
21 = 7 * 3
49 = 7 * 7
45 = 3 * 3 * 5
so, (105)^3 = 3 * 7 * 7 * 7 * 3 *3 *5 *b
Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5 * 7^3 *b
Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 * 7^3
b = 5^2 = 25
Correct answer A.
Answer: (A) 25
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers Q are there between 6* + 2 and 6* + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes Q in this range.
Answer: A.
Answer: (A) None
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
(A) 287 sq.cm
(B) 655 sq.cm
(C) 654 sq.cm
(D) 600 sq.cm
(E) 266 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer: D
Answer: (D) 600 sq.cm
Question: A certain no. when divided by 80 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 3
(B) 4
(C) 6
(D) 7
(E) 9
Rationale: Explanation:
80 + 25 = 105/15 = 7 (Remainder)
D
Answer: (D) 7
Question: A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, 3, 5, and 6 at all. If repeated digits are allowed, what is the probability that it has at least one even digit?
(A) 97/100
(B) 121/125
(C) 343/400
(D) 609/625
(E) 729/1000
Rationale: P(no even digits) = 2/5*2/5*2/5*2/5 = 16/625
P(at least one even digit) = 1 - 16/625 = 609/625
The answer is D.
Answer: (D) 609/625
Question: A and B can do a piece of work in 2 days, B and C in 3 days, C and A in 4 days. How long will C take to do it?
(A) 14 days
(B) 20 days
(C) 22 days
(D) 24 days
(E) 26 days
Rationale: 2c = 1/3 + 1/4 – 1/2 = 1/12
c = 1/24 => 24 days
ANSWER:D
Answer: (D) 24 days
Question: Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 120. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?
(A) (a)100
(B) (b) 81
(C) (c) 82
(D) (d) 83
(E) (e) 84
Rationale: T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets. We have (120-6)/6+1=20 such multiples.
So, final number of sets is 20*5=100
Answer: A
Answer: (A) (a)100
Question: Set J consists of 15 consecutive even numbers. If the smallest term in the set is -10, what is the range of the positive integers in set J?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 20
Rationale: Since there are only 15 integers, another approach is the just list all 15.
We get:-10, -8, -6, -4, -2,0,2, 4, 6, 8, 10, 12, 14, 16, 18
Range of POSITIVE INTEGERS =18 - 2= 16
Answer: D
Answer: (D) 16
Question: The age of Ram and Suba are in the ratio 5:6 and after 4 years their ratios are 7:8 then what is the present age of Suba?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Let ages of Ram and Suba are R & S respectively, then
R/S = 5/6 => R = (5/6)*S -------(1)
after 4 years,
(R+4)/(S+4) = 7/8
=> 8R+32 = 7S+28
=> 8*5S/6 = 7S - 4 [from (1)]
=> 20S = 21S - 12
=> S = 12
present age of Suba = S = 12 Years
ANSWER:B
Answer: (B) 12
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 22.4
(B) 22.9
(C) 22.2
(D) 79.2
(E) 23.7
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer:D
Answer: (D) 79.2
Question: Rs 3200 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
(A) s 400
(B) s 200
(C) s 800
(D) s 500
(E) s 100
Rationale: Explanation :
Average rate = (144/3200)*100 = 4.5
Ratio = 5:15
So, first part = (5/20)*3200 = Rs 800.
Answer :C
Answer: (C) s 800
Question: Find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5.
(A) 128
(B) 197
(C) 127
(D) 182
(E) 091
Rationale: Explanation:
Let 'N' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5.
Required number = (LCM of 13 and 16) - (common difference of divisors and remainders) = (208) - (11) = 197.
Answer:B
Answer: (B) 197
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations of soloists can appear in the liner notes?
(A) 5!
(B) 10!/(5!5!)
(C) 10!
(D) 10!*5!
(E) 5!*5!
Rationale: There are 10 soloists ------------- (1)
Room available is only for 5 soloists -------------- (2)
There is no issue for sequencing, i.e selected 5 soloists say for eg : A,B,C,D,E are same as C,E,D,B,A
Therefore from (1) & (2),
Number of ways of selecting 5 different soloists from 10 is 10C5
= 10!/(5!*5!)
ANSWER:B
Answer: (B) 10!/(5!5!)
Question: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 30 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
(A) 3/200
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
Rationale: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 30/100 = 3/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) Ã—(1/5) Ã— (3/10) = 3/200
Answer: A
Answer: (A) 3/200
Question: What is the present worth of Rs. 154 due in 2 years at 5% simple interest per annum
(A) 110
(B) 120
(C) 130
(D) 140
(E) None of these
Rationale: Explanation:
Let the present worth be Rs.x
Then,S.I.= Rs.(154 - x)
= (x*5*2/100) = 154 - x
= 10x = 15400 - 100x
= 110x = 15400
x= 140
Answer: D
Answer: (D) 140
Question: A man24years older than his son. In two years, his age will be twice the age of his son. The present age of the son is ?
(A) 17years
(B) 15yeras
(C) 31years
(D) 29years
(E) 22years
Rationale: Let the son's present age be x
Then , man's present age = x+24
(x+24)+2 = 2(x+2)
x+26 = 2x+4
x = 22
Answer is E
Answer: (E) 22years
Question: The H.C.F. of two numbers is 16 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 224
(D) 345
(E) 365
Rationale: Clearly, the numbers are (16 x 13) and (16 x 14).
Larger number = (23 x 14) = 224. Answer: Option C
Answer: (C) 224
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
(A) 19
(B) 81
(C) 12
(D) 13
(E) 17
Rationale: d2 = 122 + 42 + 32
= 13
Answer:D
Answer: (D) 13
Question: P, Q, R subscribe Rs. 50,000 for a business. P subscribes Rs. 4000 more than Q and Q Rs. 5000 more than R. Out of a total profit of Rs. 25,000, what will be P's share?
(A) Rs. 8400
(B) Rs. 10,500
(C) Rs. 13,600
(D) Rs. 14,700
(E) None of these
Rationale: Explanation:
Let amount subscribed for R be x.
Therefore, Q = x + 5000 and P = x + 5000 + 4000 = x + 9000
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
P : Q : R = 21000 : 17000 : 12000 = 21 : 17 : 12
P’s share = 25000 X (21/50) = Rs. 10,500
ANSWER B
Answer: (B) Rs. 10,500
Question: the hiker walking at a constant rate of 6 miles per hour is passed by a motor-cyclist traveling in the same direction along the same path at 30 miles per hour. the motor-cyclist stops to wait for the hiker 12 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the motor-cyclist wait until the hiker catches up?
(A) 30
(B) 36
(C) 40
(D) 48
(E) 60
Rationale: For the 12 minutes the motor-cyclist continues to overtake the hiker, she is going at 24 miles per hour faster than the hiker.
Once the motor-cyclist stops, the hiker is going at 6 miles per hour while the motor-cyclist is at rest
So the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds. 24/6 * 12 or 48 minutes
Answer is (D)
Answer: (D) 48
Question: In a box, there are 3 blue, 4 white and 6 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?
(A) 3/16
(B) 5/16
(C) 6/13
(D) 6/15
(E) 9/32
Rationale: Total number of bulbs = (3 + 4 + 6) = 13.
Let E = event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.
Therefore, P(E)=6/13
ANSWER:C
Answer: (C) 6/13
Question: What proximate value should come in place of the question mark (?) in the following question?
9.595 Ã— 1084 + 2568.34 â€“ 1708.34 = ?
(A) 6,000
(B) 12,000
(C) 10,000
(D) 11228
(E) 22397
Rationale: ? â‰ˆ 9.6 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 10368 + 860 â‰ˆ 11228
Answer D
Answer: (D) 11228
Question: The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
(A) 21
(B) 23
(C) 26
(D) 29
(E) 30
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
Number to be added = (60 - 37) = 23.
answer :B
Answer: (B) 23
Question: Tim has 3 dogs named Rocky, Dash and Tango. Rocky and Dash together weigh 120 pounds. Dash and Tango
together weigh 280 pounds. All three together weigh 310 pounds. What is Dash’s weight?
(A) 30 lbs
(B) 45 lbs
(C) 60 lbs
(D) 80 lbs
(E) 90 lb
Rationale: Given:
Weight of Rocky + Dash = 120 ----- (i)
Weight of Dash + Tango = 280 ----- (ii)
Weight of Rocky + Dash + Tango = 310 ----- (iii)
Putting the value of Rocky + Dash from equation (i) in equation (iii)
120 + Tango = 310
Tango = 190 lbs
Now putting the value of Tango in equation (ii)
Dash + 190 = 280
Dash = 90lbs
Option E
Answer: (E) 90 lb
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
(A) 27729
(B) 27772
(C) 12992
(D) 13500
(E) 26782
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500.Answer: D
Answer: (D) 13500
Question: P, Q, R enter into a partnership and their share are in the ratio 1/2:1/3:1/4. After two months, P withdraws half of his capital and after 10 more months, a profit of Rs 378 is divided among them. What is Q's share?
(A) 121
(B) 156
(C) 169
(D) 148
(E) 144
Rationale: The ratio of their initial investment
=1/2:1/3:1/4=6:4:3
Let the initial investment of P, Q and R be 6x,4x and 3x respectively.
A:B:C
=(6x×2+3x×10):4x×12:3x×12
=(12+30):4×12:3×12=(4+10):4×4:12=14:16:12=7:8:6
B's share =378×8/21=18×8=144
Answer is E.
Answer: (E) 144
Question: Three unbased coins are tossed. the probability of getting at most one tail and two head is ?
(A) 3/8
(B) 7/8
(C) 3/4
(D) 1/5
(E) 2/3
Rationale: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {THH,HTH,HHT}
P(E)=n(E)/n(S)=3/8
Answer(A)
Answer: (A) 3/8
Question: The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?
(A) 80,70 kmph
(B) 80,40 kmph
(C) 10,40 kmph
(D) 80,80 kmph
(E) 90,30 kmph
Rationale: Speed downstream = 60 + 30
= 90 kmph
Speed upstream = 60 - 30
= 30 kmph
Answer: E
Answer: (E) 90,30 kmph
Question: Jane makes toy bears. When she works with an assistant, she makes 100 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
(A) 20%
(B) 80%
(C) 100%
(D) 180%
(E) 200%
Rationale: We can use fractional equivalents here to solve the problem
80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears
10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours
Now we come to productivity
Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour
Hence the productivity is double with the assistant i.e. the increase in productivity is 200%
E
Answer: (E) 200%
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon (10-sided polygon)?
(A) 3/10
(B) 2/5
(C) 2/7
(D) 10/21
(E) 5/11
Rationale: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.
So the remaining n-3 vertices make diagonals.
There are 2 of these diagonals which are the shortest.
The probability of choosing one of the shortest diagonals is 2/7.
The answer is C.
Answer: (C) 2/7
Question: A 50-liter solution of milk and water is 5 percent alcohol. If 1.5 liters of milk and 8.5 liters of water are added to this solution, what percent of the solution produced is milk?
(A) 5.5%
(B) 6%
(C) 6 1/3%
(D) 6 1/5%
(E) 6 2/3%
Rationale: 5% milk in 50 litre solution = 2.5 litres
adding 1.5 litres to it makes it total of 4 litres
total solution = 60 litres
% milk = 4/60 * 100 = 6.666667%
Answer - E
Answer: (E) 6 2/3%
Question: The price of a TV was increased by 30 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?
(A) 82%
(B) 75%
(C) 65%
(D) 50%
(E) 45%
Rationale: consider base price - $100
30% increase = 1.30*100 = $130
another 40% increase on new price = 1.4* 130 = $182
so final price of radio - $182
therefore a 82% increase
correct option - A
Answer: (A) 82%
Question: A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
(A) Rs. 120
(B) Rs. 121
(C) Rs. 122
(D) Rs. 123
(E) Rs. 124
Rationale: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]
= [1600 * 41/40(41/40 + 1)
= [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.
C.I. = 3321 - 3200 = Rs. 121.
ANSWER:B
Answer: (B) Rs. 121
Question: How many arrangements of the letters of the word GUIDE can be made, without changing the place of the vowels in the word?
(A) 4
(B) 6
(C) 2
(D) 3
(E) 5
Rationale: U,I,E fixed. Consonants can be arrangements in 2p2 = 2! = 2 ways
Option 'C'
Answer: (C) 2
Question: A train 250 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
(A) 6 sec.
(B) 7 sec.
(C) 9 sec.
(D) 15 sec.
(E) None
Rationale: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 250 m at (50 /3)m/sec
= (250 x 3/50)sec
= 15 sec.
Answer D
Answer: (D) 15 sec.
Question: There are 600 military people in a division of the army. There is one Officer for every 23 soldiers in that division. Now the question is how many officers are in the division?
(A) 22
(B) 35
(C) 37
(D) 73
(E) 25
Rationale: E
25
23 soldiers + 1 officer makes a group of 24 people. Now number of such groups = 600/24 = 25.
Answer: (E) 25
Question: After decreasing 24% in the price of an article costs Rs.836. Find the actual cost of an article?
(A) 1667
(B) 6789
(C) 1200
(D) 1100
(E) 1421
Rationale: CP* (76/100)
= 836
CP= 11 * 100 => CP
= 1100
Answer: D
Answer: (D) 1100