mathewhe/aqua_rat huggingface dataset:
Question: A cab driver 5days income was $300, $150, $750, $400 , $500. Then his average income is?
(A) $500
(B) $650
(C) $420
(D) $375
(E) $625
Rationale: avg = sum of observations/number of observations
avg income=(300+150+750+400+500)/5 = 420
Answer is C
Answer: (C) $420
Question: By how much is 50% of 250 greater than 25% of 400.
(A) 25
(B) 26
(C) 29
(D) 39
(E) 26
Rationale: (50/100) * 250 â€“ (25/100) * 400
125 - 100 = 25
Answer:B
Answer: (B) 26
Question: What is the middle number in a sequence of 11 integers with a total sum 99?
(A) 12
(B) 9
(C) 5.5
(D) 7
(E) 8
Rationale: The average or median is: 99/11 = 9 , which is the middle in the sequence.
Answer: B
Answer: (B) 9
Question: A 5-letter code word consists of letters A, B, and C. If the code includes all the three letters, how many such codes are possible?
(A) 90
(B) 48
(C) 36
(D) 24
(E) 18
Rationale: Note that the correct answer to this question is 36, not 72.
AB-ABC can be arranged in 5!/2!2!=30 ways;
BC-ABC can be arranged in 5!/2!2!=30 ways;
AC-ABC can be arranged in 5!/2!2!=30 ways;
Total: 30+30+30=90.
Answer: A.
Answer: (A) 90
Question: If f, g, and h are positive numbers such that (f/(f+g))(10) + (g/(f+g))(20)=h and if f<g which of the following could be the value of h?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 30
Rationale: The answer is D. For any positive f and g, h is a number between 10 and 20. Since f < g, weight of 10 is inferior of weight of 20 -> h is > 15 -> 18 is the answer.
Answer: (D) 18
Question: 8597 - ? = 7429 - 4358
(A) 5526
(B) 5536
(C) 5556
(D) 5576
(E) 5586
Rationale: Let 8597 - x = 7429 - 4358.
Then, x = (8597 + 4358) - 7429
= 12955 - 7429 = 5526.
Answer is A
Answer: (A) 5526
Question: A football team lost 5 yards and then gained 10. What is the team's progress?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: For lost, use negative. For gain, use positive.
Progress = -5 + 10 = 5 yards
C
Answer: (C) 5
Question: A man can row downstream at the rate of 45 Kmph and upstream at 23 Kmph. Find the man’s rate in still water and rate of current?
(A) 8.5
(B) 10.0
(C) 12.5
(D) 11.0
(E) 8.25
Rationale: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (45 + 23) = 34 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (45 - 23)
= 1/2 (22)
= 11 kmph
Answer is D.
Answer: (D) 11.0
Question: How is 5% expressed as a decimal fraction?
(A) 0.5
(B) 0.05
(C) 0.005
(D) 0.0005
(E) 5
Rationale: 5/100= 0.05
ANSWER:B
Answer: (B) 0.05
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number T of ways this can be done is:
(A) 122
(B) 210
(C) 216
(D) 217
(E) 225
Rationale: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216=Y
Answer: C.
Answer: (C) 216
Question: A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 104 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: We have to work with multiples of 20 and 25.
First, we must know the limits of this multiples, so:
105/25= 4....so the max is 4
105/20=5...so the max is 5
105-100 =5
Answer : E
Answer: (E) 5
Question: A train 100 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 28
(B) 50
(C) 88
(D) 41
(E) 12
Rationale: Speed of the train relative to man = (100/10) m/sec = (10) m/sec. [(10) * (18/5)] km/hr = 36 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 36 ==> x
= 41 km/hr.Answer:D
Answer: (D) 41
Question: A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water
(A) 15 km/hr
(B) 12 km/hr
(C) 13 km/hr
(D) 14 km/hr
(E) None of these
Rationale: Explanation :
Let the speed of the water in still water = x
Given that speed of the stream = 3 kmph
Speed downstream = (x+3) kmph
Speed upstream = (x-3) kmph
He travels a certain distance downstream in 4 hour and come back in 6 hour.
ie, distance travelled downstream in 4 hour = distance travelled upstream in 6 hour
since distance = speed × time, we have
(x+3)4=(x−3)6
=> (x + 3)2 = (x - 3)3
=> 2x + 6 = 3x - 9
=> x = 6+9 = 15 kmph. Answer : Option A
Answer: (A) 15 km/hr
Question: 11:35::17:?
(A) 3
(B) 22
(C) 58
(D) 10
(E) 54
Rationale: 11:35::17:X
11x:35x17
11x=595
x=54
ANSWER:D
Answer: (D) 10
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 4 inches tall. How tall are the sculpture andbase together?
(A) 3.17 feet
(B) 3.2 feet
(C) 3.3 feet
(D) 3.4 feet
(E) 3.5 feet
Rationale: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+4=38
38/12=3.17 feet
ANSWER:A
Answer: (A) 3.17 feet
Question: By investing in 1623% stock at 64, one earns Rs. 1800. The investment made is
(A) s. 6500
(B) s. 7500
(C) s. 5640
(D) s. 5760
(E) s. 6912
Rationale: Explanation :
Market Value = Rs.64
Face Value is not given and hence take it as Rs.100
16 2/3% of the face value = 50/3
ie, to earn 50/3, investment = Rs.64
Hence, to earn Rs.1800, investment needed = 64×3×1800/50 = 6912
Answer : Option E
Answer: (E) s. 6912
Question: Two stations A and B are 200 km apart on a straight track. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 02 p.m.
(B) 06 p.m.
(C) 10 p.m.
(D) 12 p.m.
(E) 11 p.m.
Rationale: Explanation:
Assume both trains meet after 'p' hours after 7 a.m.
Distance covered by train starting from A in 'p' hours = 20p km
Distance covered by train starting from B in (p-1) hours = 25(p-1)
Total distance = 200
=> 20x + 25(x-1) = 200
=> 45x = 225
=> p= 5
Means, they meet after 5 hours after 7 am, ie, they meet at 12 p.m.
Answer: D
Answer: (D) 12 p.m.
Question: Find the number of solutions for 3x+4y=60, if x and y are positive integers
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 3x+4y=60
=>x=(60-4y)/3
as x and y are positive integers, put y=1,2,3,... & find x
y=3,x=16
y=6,x=12
y=9,x=8
y=12,x=4
(x,y)=(4,12),(8,9),(12,6),(16,3)
only 4 solution
ANSWER:D
Answer: (D) 4
Question: 0, 1, 4, 9, 16, 25, 36, 49, ?What number should replace the question mark?
(A) 81
(B) 74
(C) 64
(D) 24
(E) 48
Rationale: C 64add 0^2,1^2,2^2,......
Answer: (C) 64
Question: A can contains a mixture of liquids A and B is the ratio 7:5. When 3 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter of liquid A was contained by the can initially?
(A) 7
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Ci*Vi = Cf*Vf
(7/12)*(V1 - 3) = (7/16)*V1
(V1 - 3)/V1 = 3/4
3 accounts for the difference of 1 on ratio scale so Initial volume = V1 = 4*3 = 12 litres.
7/12 of the initial mixture was liquid A so liquid A was (7/12)*12 = 7 litres.
Answer : A
Answer: (A) 7
Question: If the area of a square with sides of length 11 centimeters is equal to the area of a rectangle with a width of 11 centimeters, what is the length of the rectangle, in centimeters?
(A) 4
(B) 8
(C) 11
(D) 16
(E) 18
Rationale: Let length of rectangle = L
11^2 = L*11
=> L = 121/11 = 11
Answer C
Answer: (C) 11
Question: (3080 + 6160) / 28
(A) 380
(B) 350
(C) 330
(D) 310
(E) None of these
Rationale: Explanation:
As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9240)/28 = 330
Option C
Answer: (C) 330
Question: How many 3 digit numbers are divisible by 6 in all ?
(A) 150
(B) 111
(C) 120
(D) 243
(E) 345
Rationale: A
150
Required numbers are 102, 108, 114, ... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n.
Then, a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150.
Answer: (A) 150
Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
(A) 3/13
(B) 1/13
(C) 2/11
(D) 3
(E) 2
Rationale: Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/52	= 3/13
Hence Answer is A
Answer: (A) 3/13
Question: What should come in place of the question mark (?) in the following equation?
9548 + 7314 = 8362 + ?
(A) 8230
(B) 8500
(C) 8410
(D) 8600
(E) None of these
Rationale: 9548 + 7314 = 8362 + ?
or,? = 9548 + 7314 – 8362 = 8500
Answer B
Answer: (B) 8500
Question: During a Pizza buffet where A eats more times 4 than B, and B eats 8 times less than C.find the least number of times all the three has to eat
(A) 7
(B) 5
(C) 9
(D) 2
(E) 4
Rationale: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 4:1 and as B eat 8 times less the C the the ratio of B : C is 1:8 the the least number of times all three has eat is the LCM of A,B,C that is 8 ..
ANSWER:E
Answer: (E) 4
Question: The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2. What is the total of P's and Q's present ages?
(A) 48 years
(B) 65 years
(C) 87 years
(D) 20 years
(E) 26 years
Rationale: Let the present ages of P and Q be 5x and 7x years respectively.
Then, 7x - (5x + 6) = 2
2x = 8 => x = 4
Required sum = 5x + 7x = 12x = 48 years.
Answer:A
Answer: (A) 48 years
Question: A pipe can fill a cistern in 12 minutes whereas the cistern when fill can be emptied by a leak in 18 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17
(B) 16
(C) 70
(D) 36
(E) 12
Rationale: 1/12 - 1/18 = 1/36
36 minutes
Answer: D
Answer: (D) 36
Question: Tommo spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommo won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
(A) 330
(B) 500
(C) 520
(D) 540
(E) 620
Rationale: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, tommo earned$520. Answer choice C.
Answer: (C) 520
Question: Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 4w widgets?
(A) 4
(B) 6
(C) 8
(D) 24
(E) 12
Rationale: Let Y produce w widgets in y Days
Hence, in 1 day Y will produce w/y widgets.
Also, X will produce w widgets in y+2 days (given, X takes two more days)
Hence, in 1 day X will produce w/y+2 widgets.
Hence together X and Y in 1 day will produce {w/y + w/y+2} widgets.
Together X and Y in 3 days will produce = 3 * [{w/y + w/y+2}] widgets.
It is given that in 3 days together they produce (5/4)w widgets.
Equating, 3 * [{w/y + w/y+2}] = (5/4)w
Take out w common and move 3 to denominator of RHS
w{1/y + 1/(y+2)} = (5/12)w
Canceling w from both sides
{1/y + 1/(y+2)} = 5/12
2y+2/y(y+2) = 5/12
24y+24=5y^2 + 10y
5y^2-14y-24=0
5y^2-20y+6y-24=0
5y(y-4)+6(y-4)=0
(5y+6)+(y-4)=0
y=-6/5 or y=4
Discarding y=-6/5 as no of days cannot be negative
y=4
hence it takes Y, 4 days to produce w widgets.
Therefore, it will take X (4+2)=6 days to produce w widgets.
Hence it will take X 4*6=24 days to produce 4w widgets.
Answer : D
Answer: (D) 24
Question: A bus moving at a speed of 45 km/hr. overtakes a truck 150 metres ahead going in the same directions in 30 seconds. The speed of the truck is
(A) 27km/hr
(B) 24km/hr
(C) 25km/hr
(D) 28km/hr
(E) None of these
Rationale: Explanation:
The lag of 150 m has been covered by the bus in 30 seconds.
Therefore, the relative speed of the bus and truck is =(5X18)/5=18km/h
The speed of truck is 45-18 = 27 Km/hr
Answer A
Answer: (A) 27km/hr
Question: In triangle PQR, the angle Q = 90 degree, PQ =3 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
(A) 3.6 cm
(B) 2.4 cm
(C) 4.8 cm
(D) 2.16 cm
(E) 3.2 cm
Rationale: Look at the diagram below:
Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:3=8:10 --> QY=2.4.
Answer: B.
Answer: (B) 2.4 cm
Question: The original price of a suit is $200. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit?
(A) $178.50
(B) $182.50
(C) $185.50
(D) $187.50
(E) $200
Rationale: 0.75*(1.25*200) = $187.50
The answer is D.
Answer: (D) $187.50
Question: In Town X, 64 percent of the population are employed, and 55 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 14%
(B) 25%
(C) 32%
(D) 40%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 55 are employed males, hence 9% are employed females.
(employed females)/(total employed people)=9/64=14%
Answer: A.
Answer: (A) 14%
Question: If the integer N = 139,k50 where k is the hundreds digit, N can NEVER be divisible by which of the following?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: It is divisible by 2 irrespective of k value as unit digit's value is even(0).
It can be divisible by 3 for k values 2,5,8 as sum will be divisible by 3
It can be divisible by 6 if divisible by 2 and 3.
It can be divisible by 9 for k value 2 as sum will be divisible by 9.
Therefore answer is 4 as number is divisible if last two digits are divisible.In this case 50(No)
Hence answer C
Answer: (C) 4
Question: A bike owner buys petrol at Rs 75, Rs. 80 and Rs. 85 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 40000 each year?
(A) Rs 79.8
(B) Rs 80.4
(C) Rs 85.5
(D) Rs 90
(E) Rs 60
Rationale: Explanation :
Total quantity of petrol consumed in 3 years = 40000/75 + 40000/80 + 40000/85 litres
= 40000 (1/75 + 1/80 + 1/85 ) = 40000(767/20,400) = 76700/51 litres
Total amount spent = Rs. (3 x 40000) = Rs. 120000.
Average cost = Rs. 120000 x 51/76700
= Rs. 61200/767
= Rs. 79.8
Answer : A
Answer: (A) Rs 79.8
Question: The equation a = 2y2 + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at a = -5, the equation for l is
(A) + y + 15 = 0
(B) - 3x - 11 = 0
(C) + y - 16.5 = 0
(D) - y - 7 = 0
(E) + y + 13.5 = 0
Rationale: Is optionC: -3a + y -6.5= 0=c
Answer: (C) + y - 16.5 = 0
Question: The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination
(A) 15 years
(B) 16 years
(C) 14 years 8 month
(D) 16 years 2 month
(E) 19 years 8 month
Rationale: (d) Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
2.(a) Total increase = 8 * 2 = 16 years
So, total age of two women = 35 + 45 +16= 96
Average age of two women=96/2=48 years
3(d) Total decrease = 20 * 2 = 40 month
= 3 years 4 month
So, age of new boy = 18 years – 3 years 4 month
= 14 years 8 month
C
Answer: (C) 14 years 8 month
Question: What should come next in the following letter sequence?
A A B A B C A B C D A B C D E A B C D
(A) T
(B) E
(C) H
(D) F
(E) V
Rationale: Answer: B)
Answer: (B) E
Question: Find the value of (55 + 113/78) × 78
(A) 4423
(B) 4403
(C) 4413
(D) 2403
(E) 4375
Rationale: =(55 + 113/78) × 78
=(4290 + 113)/78 × 78
=4403/78× 78
=4403
Answer is B.
Answer: (B) 4403
Question: 3 men can complete a piece of work in 6 days. Two days after they started the work, 3 more men joined them. How many days will they take to complete the remaining work?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
3 man 1 day work = 1616
3 man 2 days work = 2626
Remaining work = (1 – 2626 ) = 2/3 parts.
6 man together perform the work in 1 day is = 1616 + 1616 = 2626 parts
2626 parts completed in 1 day
2323 parts will b completed in 2 days
Answer:A
Answer: (A) 2
Question: If n is a prime number, which of the following could be true
(A) n^n=n
(B) n^n/4 = 1^(n-1)
(C) (n)(n^n) = is negative
(D) n^2+n^3= n^5
(E) n^2/4= is even
Rationale: B should be the answer.
2^2/4 = 1^(2-1)
Answer: (B) n^n/4 = 1^(n-1)
Question: The vertex of a parallelogram are (1, 0), (3, 0), (1, 1) and (3, 1) respectively. If line L passes through the origin and divided the parallelogram into two identical quadrilaterals, what is the slope of line L?
(A) . 1/2
(B) 2
(C) 1/4
(D) 3
(E) 3/4
Rationale: Soln:-
Added the line BE (the required line that divides the given parallelogram into 2 identical quadrilaterals).
Careful observation reveals that slope of the diagonal AD = (1-0)/(3-1) = 0.5. Thus the slope of line BE should be < slope of AD
Only option C is < 0.5 and is thus the correct answer.
Answer: (C) 1/4
Question: If a man can cover 14 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 288
(B) 162
(C) 189
(D) 168
(E) 122
Rationale: 14 m/s = 14 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 14 * 18/5 * 15/4 km = 189 km.
Answer: C
Answer: (C) 189
Question: For positive integers n, the integer part of the nth term of sequence D equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, D_1 = 1.2345678…, while D_2 = 2.4681012… The sum of the first seven terms of sequence D is between:
(A) 28 and 29
(B) 29 and 30
(C) 30 and 31
(D) 31 and 32
(E) 32 and 33
Rationale: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
D_1 = 1.23…
D_2 = 2.46…
D_3 = 3.69…
D_4 = 4.812…
D_5 = 5.10…
D_6 = 6.12…
D_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
Answer: (C) 30 and 31
Question: An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of
(A) 580 Kmph
(B) 550 Kmph
(C) 540 Kmph
(D) 530 Kmph
(E) 520 kmph
Rationale: Explanation:
Speed of aeroplane = 420 Kmph
Distance travelled in 6 hours
= 420 * 6 = 2520 Km
Speed of aeroplane to acver 2520 Km in 14/3
= 2520*3/14 = 540 Km
Answer: Option C
Answer: (C) 540 Kmph
Question: price of apple mobile is double than samsung and triple than oppo.the mean off all three phone's price is 25000.what is price of samsung.
(A) 21,200.20
(B) 22,000
(C) 20,454.54
(D) 23,300.33
(E) 24,000
Rationale: solution
let the price of oppo is x,then price of apple 3x and price of samsung 1.5x
(x+3x+1.5x)/3=25000
5.5x=75000
x=75000/5.5=13,636.36
Samsung price=1.5x=20,454.54
answer C
Answer: (C) 20,454.54
Question: The area of a triangle is with base 4m and height 5m?
(A) 76 m2
(B) 10 m2
(C) 27 m2
(D) 18 m2
(E) 17 m2
Rationale: 1/2 * 4 * 5 = 10 m2
Answer:B
Answer: (B) 10 m2
Question: an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -w and a*w=0, then w=?
(A) a) -a
(B) b) -1/a
(C) c) 1/a
(D) d)0
(E) e)a
Rationale: If a*w=0 and a=-w then a-w = o of a=w, so answer E
Answer: (E) e)a
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 520 kms in 4 hours, then the speed of the first train is:
(A) 89.25 km/hr.
(B) 37.25 km/hr.
(C) 90.25 km/hr.
(D) 113.75 km/hr.
(E) 96.25 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (520/4) = 130
x = (130/8) = 16.25
Hence, speed of first bullet train = (7 x 16.25) km/hr = 113.75 km/hr.
D
Answer: (D) 113.75 km/hr.
Question: Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents Z watch all of the shows?
(A)  150
(B)  108
(C)  42
(D)  21
(E)  -21
Rationale: OA is D.
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is Z =3.5% of 600, is 21. D is the correct answer
Answer: (D)  21
Question: If a and b are both negative and ab < b^2, which of the following must be true?
(A) a < b < a^2 < b^2
(B) a < b < b^2 < a^2
(C) b < a < a^2 < b^2
(D) a^2 < b^2 < b < a
(E) b^2 < a^2 < b < a
Rationale: Because ab < b^2 and both are negative, I thought a < b. So I crossed off answers c), d), and e).
And because a < b , a^2 < b^2
ans C
Answer: (C) b < a < a^2 < b^2
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 17%, then the cost price of the article is:
(A) 500
(B) 334
(C) 555
(D) 664
(E) 526
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/117 = Rs. 526
Answer: Option E
Answer: (E) 526
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
(A) 12.9
(B) 12.0
(C) 12.5
(D) 12.2
(E) 12.1
Rationale: 1000*15 = 1200*x
x = 12.5
Answer:C
Answer: (C) 12.5
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
(A) 29
(B) 37
(C) 54
(D) 42
(E) 60
Rationale: After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
125 : 150 :: 35 : x
125 * x = 150 x 35
x =	(150 x 35)/125
x = 42.
Answer is D.
Answer: (D) 42
Question: The average age of students of a class is 15.7 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
(A) 3:7
(B) 7:3
(C) 2:5
(D) 2:1
(E) 2:4
Rationale: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.7
= (16.4 - 15.7)k = (15.7 - 15.4)
= k = 0.3/0.7 = 3/7
Required ratio = 3/7 : 1 = 3:7.
Answer:A
Answer: (A) 3:7