mathewhe/aqua_rat huggingface dataset:
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
(A) 298
(B) 207
(C) 238
(D) 205
(E) 293
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer:D
Answer: (D) 205
Question: In a renowned city, the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A) 32,300
(B) 172,800
(C) 468,830
(D) 86,400
(E) 259,200
Rationale: Every 2 seconds, 2 persons are added (8-6). Every second 1 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 1 = 86400
Option D
Answer: (D) 86,400
Question: A and B started a business with initial investments in the ratio 4 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?
(A) 6 months
(B) 8 months
(C) 9 months
(D) 5 months
(E) 14 months
Rationale: Let Sumit in the business for ‘a’ months.
Investment Ratio Amit to Sumith = 4 : 3.
Profit sharing ratio = 8 : 7.
Amit is in the business for 12 months.
Then Sumit in the business for
(4 × 12) / (3 × a) = 8 / 7 => 24a = 336 or
a = 336 / 24 = 14 or 14 months
Option E
Answer: (E) 14 months
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
(A) 33 days
(B) 77 days
(C) 99 days
(D) 11 days
(E) 18 days
Rationale: x/24 + x/30 + x/40 = 1
x = 11 days
Answer: D
Answer: (D) 11 days
Question: In how many of ways can 4 balls be placed in 4 tins if any number of balls can be placed in any tin?
(A)  5C4
(B)  5P4
(C)  54
(D)  4^4
(E)  5^5
Rationale: Now, each of the 4 different balls has 4 choices (4 tins to go to), so total # of distribution is 4*4*4*4=4^4.
Answer: D.
Answer: (D)  4^4
Question: 5^4 + 5^4 + 5^4 + 5^4 =
(A) 5^5
(B) 5^6
(C) 4^8
(D) 4^9
(E) 4^12
Rationale: Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
5^4 + 5^4 + 5^4 + 5^4 =
Now, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...
X + X + X + X =
What would the sum be?
Clearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...
5^4 + 5^4 + 5^4 + 5^4 =
5(5^4)
This can be re-written as...
(5^1)(5^4)
...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...
(5^1)(5^4) = 5^5
Final Answer:
A
Answer: (A) 5^5
Question: A train is moving at the speed of 80 km/hr. What is its speed in metres per second?
(A) 22 2/9 m/s
(B) 22 8/9 m/s
(C) 22 2/7 m/s
(D) 22 2/5 m/s
(E) 22 3/9 m/s
Rationale: Speed = 80 km/hr = 80×518 m/s = 40×59 m/s = 2009 m/s = 22 2/9 m/s
Answer : A
Answer: (A) 22 2/9 m/s
Question: The length of a side of a hexagon is 2 inches. What is the perimeter?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Hexagon. It means 6 equal sides.
p = 2 + 2 + 2 + 2 + 2 + 2 = 4 + 4 + 4 = 8 + 4 = 12 inches
Answer B
Answer: (B) 12
Question: Find the constant k so that : -x2 - (k + 7)x - 8 = -(x - 2)(x - 4)
(A) -11
(B) -12
(C) -13
(D) -14
(E) -15
Rationale: -x2 - (k + 7)x - 8 = -(x - 2)(x - 4) : given
-x2 - (k + 7)x - 8 = -x2 + 6x - 8
-(k + 7) = 6 : two polynomials are equal if their corresponding coefficients are equal.
k = -13 : solve the above for k
correct answer C
Answer: (C) -13
Question: Find out the square of a number which when doubled exceeds its one seventh by 13 ?
(A) 16
(B) 49
(C) 19
(D) 26
(E) 17
Rationale: A
Let the number be p, then the square will be p^2
According to question:
2p = (p/7) + 13
=> 14p = p +91
=> p = 7
p^2 = 7^2 = 49.
Answer : B
Answer: (B) 49
Question: The average of a set of five distinct integers is 350. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?
(A) -4,244
(B) -3,997
(C) -3,494
(D) -3,194
(E) The answer cannot be determined from the information given
Rationale: Sum of the set = 350*5=1750 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 1750-5994= -4244
Answer=A
Answer: (A) -4,244
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43, 46, 51 x
(A) 29
(B) 31
(C) 23
(D) 54
(E) 59
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 51 + 3 = 54.
Answer: (D) 54
Question: In the biology lab of "Jefferson" High School there are 1.08*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
(A) 100
(B) 200
(C) 500
(D) 1000
(E) 5000
Rationale: 1.08*10^6/ 10800==> 10.8*10^3/108==> 10800/108= 100
ANSWER:A
Answer: (A) 100
Question: Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week?
(A) Rs.150
(B) Rs.220
(C) Rs.250
(D) Rs.300
(E) Rs.310
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C)
Answer: (C) Rs.250
Question: P is three times as fast as Q and working together, they can complete a work in 15 days. In how many days can Q alone complete the work?
(A) 16 days
(B) 17 days
(C) 19 days
(D) 14 days
(E) 20 days
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 15 days, which means Q can do the work in 60 days.
Hence, P can do the work in 20 days.
Answer:E
Answer: (E) 20 days
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is:
(A) Rs.120
(B) Rs. 160
(C) Rs.240
(D) Rs.300
(E) Rs.500
Rationale: Let C's share = Rs. x
Then, B's share = Rs. x/4; A's share = Rs.2/3 * x/4= Rs. x/6
Therefore x/6 + x/4 + x = 1360
17x/12 = 1360
x= 1360*12/17= Rs.960
Hence, B's share= Rs.960/4= Rs.240
ANSWER:C
Answer: (C) Rs.240
Question: Four times the first of the three consecutive even integers is 7 more than thrice the second. The third integer is
(A) 9
(B) 11
(C) 13
(D) 17
(E) 15
Rationale: Solution
Let the three integers be x, x+2, x+4 4x = 7 + 3(x+2) x = 13 Third integer is x+4 = 13+4 = 17.
Answer D
Answer: (D) 17
Question: Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 18 machines produce in 6 minutes?
(A) 1344
(B) 3360
(C) 7560
(D) 50400
(E) 67200
Rationale: 8 machines produce 560 in 1 min
8 machines produce 560* 6 in 6 min
18 machine produce 560*6*(18/8) in 6 minutes
560*6*18/8=7560 answer is C.
Answer: (C) 7560
Question: A train is moving at a speed of 45km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
(A) 30sec
(B) 45sec
(C) 40sec
(D) 29sec
(E) 52sec
Rationale: Speed of the train = 45*5/18 = 25/2 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(25/2) = 40sec
Answer is C
Answer: (C) 40sec
Question: John completes a piece of work in 10 days, Jerry completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
(A) 4 days
(B) 8 days
(C) 10 days
(D) 12 days
(E) 13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
B)
Answer: (B) 8 days
Question: How many pairs t, t+1) have one or more prime factors common, where t is an integer and 2 ≤ t ≤9 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: t and t+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Answer: (A) 0
Question: In a certain Parallelogram the degree measure of one angle exceeds that of the other by 50 what is the degree measure of the smaller angle?
(A) 65
(B) 80
(C) 85
(D) 90
(E) 95
Rationale: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).
Given: x+(x+50)=180 --> x=65.
Answer: A.
Answer: (A) 65
Question: Rani worked in the Private company. At the time of Interview officer told her to give Salary Rs. 15000/- per month & Also 2-3 % to be increased in every month. she have taken 2-3 leaves. After one month she got Rs. 13950/- then How much amount increased to her? What is the percentage value?
(A) 300-1%
(B) 400- 2%
(C) 405 -3%
(D) 2150- 5%
(E) 500 - 3%
Rationale: Rani's Total Salary : 15000/-
Leave Days : 3days
3 days salary : 1500/-
Salary after leaves : 15000-1500 = 13500/-
Amount received : 13905/-
Difference amount = received amount- payable amount
ie, 13905 - 13500 = 405/-
Percentage value = 405/13500*100 = 3%
Answer is (C)
Answer: (C) 405 -3%
Question: The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
(A) 21:29
(B) 21:31
(C) 21:22
(D) 21:31
(E) 21:12
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
i.e., (120/100 * 7x) and (110/100 * 8x)
i.e., 42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer: C
Answer: (C) 21:22
Question: A taxi leaves Point A 4 hours after a bus left the same spot. The bus is traveling 30 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in two hours.
(A) 40
(B) 42
(C) 45
(D) 48
(E) 49
Rationale: Let the speed of bus be v - 30, speed of taxi be v
The bus travelled a total of 6 hrs and taxi a total of 2 hrs.
Hence 6 * (v-30) = 2v
6v - 180 = 2v
4v = 180
v = 45 mph
C
Answer: (C) 45
Question: 72 67 66 61 60 ...?
(A) 52
(B) 53
(C) 54
(D) 55
(E) 56
Rationale: Sequence = 72 67 66 61 60 55
There is 2 series :
1st series = 72 66 60 (decreasing by 6)
2nd series = 67 61 55 (decreasing by 6)
ANSWER:D
Answer: (D) 55
Question: John makes $60 a week from his job. He earns a raise andnow makes $68 a week. What is the % increase?
(A) 16.12%
(B) 16.66%
(C) 16.56%
(D) 17.66%
(E) 13.33%
Rationale: Increase = (8/60)*100 = (2/15)*100 = 13.33%.
E
Answer: (E) 13.33%
Question: If -4 < x < 8 and -6 < y < 3, which of the following specifies all the possible values of xy?
(A) -42 < xy < 21
(B) -48< xy < 24
(C) -28 < xy < 18
(D) -24 < xy < 21
(E) -24 < xy < 24
Rationale: The least value of xy is a bit more than 8*(-6)=-48 and the largest value of xy is a bit less than (-4)*(-6)=24.
Therefore -48 < xy < 24.
Answer: B.
Answer: (B) -48< xy < 24
Question: The average age of 3 children in a family is 20% of the average age of the father and the eldest child. The total age of the mother and the youngest child is 39 years. If the father's age is 26 years. What is the age of the second child?
(A) 15 years
(B) 16 years
(C) 18 years
(D) Cannot be determined
(E) None
Rationale: Solution
Since the total or average age of all the family members is not given, the given data is inadequate. So, the age of second child cannot be determined.
Answer D
Answer: (D) Cannot be determined
Question: 5n + 2 > 17 and 7n - 5 < 44; n must be between which numbers?
(A) 1 and 8
(B) 2 and 6
(C) 0 and 9
(D) 3 and 7
(E) 2 and 9
Rationale: 5n > 15 --> n > 3
7n < 49 --> n < 7
3 < n < 7
Answer: D
Answer: (D) 3 and 7
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs.35,000 respectively. Out of a total profit of Rs.13,800, Deepak’s share is _____
(A) 5400
(B) 3797
(C) 27877
(D) 2772
(E) 9911
Rationale: Explanation:
Ratio of their investments = 22500 : 35000 = 9 : 14
So Deepak' s share = 923923 × 13800 = Rs.5,400
Answer: A
Answer: (A) 5400
Question: What is the greatest value of positive integer x such that 2^x is a factor of 100^50?
(A) 70
(B) 80
(C) 90
(D) 100
(E) 120
Rationale: Put in simple words, we need to find the highest power of 2 in 100^50
100 = 2^2*5^2
Therefore 100^50 = (2^2*5^2)^50 = 2^100*5^100
Answer : D
Answer: (D) 100
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 8 km?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The swimmer can swim against the current at a speed of 4-2 = 2 km/h.
The time it will take is 8/2 = 4 hours.
The answer is D.
Answer: (D) 4
Question: The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Saransh?
(A) 30 years
(B) 32 years
(C) 34 years
(D) 38 years
(E) None
Rationale: Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10)	= 75.
‹=›9x = 45
x = 5.
∴ Saransh's present age = 4x + 10 = 30 years.
Answer A
Answer: (A) 30 years
Question: How many ways are there to award a gold and bronze medal to 10 contending teams?
(A) 10 × 9
(B) 10!/(3!7!)
(C) 10!/3!
(D) 360
(E) 300
Rationale: we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways
if gold medal is given to 1 of the teams then only possible 9 teams can be considered for bronze medal. we can do selection in 9 ways
Total number of ways to select the 3 possible medal winners = 10 * 9
Correct answer - A
Answer: (A) 10 × 9
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) Rs.62.50
(B) Rs.72.50
(C) Rs.75.00
(D) Rs.80.00
(E) Rs.85.00
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
ANSWER:A
Answer: (A) Rs.62.50
Question: What is the value of: 3^8 + 3^10 ?
(A)  7(3^8)
(B)  10(3^8)
(C)  3^18
(D)  3^80
(E)  6^18
Rationale: 3^8 + 3^10 = 3^8 (1 + 3^2) = 3^8 (1 + 9) = 10 (3^8), Answer B.
Answer: (B)  10(3^8)
Question: How many 3 digit odd numbers do not use any digit more than once
(A) 1720
(B) 216
(C) 224
(D) 2460
(E) 280
Rationale: The Way i solved it is
A B C ( hundreds, tens, units
)C can be 1 3 5 7 9 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilitie
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 7 * 8 * 5 = 280
Ans : E
Answer: (E) 280
Question: A number was divided successively in order by 4,5,6 the remainder was respectively 2,3,4 the numbers are?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 8
Rationale: let x=6q+3
then x^2=(6q+3)^2=6(6q^2+6q+1)+3
thus the remainder is 3
The Answer is(C)
Answer: (C) 3
Question: one father gave 10 cents to one son and 15 cents to another son so now what is the time
(A) Quarter to 1
(B) Quarter to 2
(C) Quarter to 3
(D) 2
(E) 1
Rationale: 10+15 = 25 cents .. one quarter given to two sons.
Quarter to 2
ANSWER:B
Answer: (B) Quarter to 2
Question: P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is
(A) Rs. 40000
(B) Rs. 50000
(C) Rs. 60000
(D) Rs. 70000
(E) None
Rationale: Solution: Let the amount invested by Q = q.
40000 : q = 2 : 3.
=> 40000/q = 2/3.
=> q = 40000 * (3/2) = Rs. 60000.
Answer: Option C
Answer: (C) Rs. 60000
Question: The decimal d is formed by writing in succession all the positive integers in descending order after the decimal point; that is d = 0.15141312111098765
What is the 19th and 20th digits of d to the right of decimal point?
(A) 32
(B) 43
(C) 54
(D) 12
(E) 21
Rationale: The descending order of numbers begins with 15.
0.15141312111098765
So, 15, 14, 13, 12, 11, 10, ...,(first 12 digits are 2 digit numbers).
Then, 9, 8, 7, 6, 5, ...,(next 5 digits are single digit numbers).
It follows that 4, 3, and 2 are the next digits, thus 3 and 2 are the 19th and 20th digits, respectively.
Answer: A
Answer: (A) 32
Question: Find the simple interest on Rs. 69,600 at 16 2/3% per annum for 9 months.
(A) s.8500
(B) s.8700
(C) s.7500
(D) s.7000
(E) s.6500
Rationale: P = Rs.69600,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(69,600*(50/3)*(3/4)*(1/100))
= Rs.8700
Answer is B.
Answer: (B) s.8700
Question: A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
(A) 252
(B) 432
(C) 462
(D) 504
(E) None
Rationale: Solution:
In order to reach (5,6) covering the shortest distance at the same time the man has to make 5 horizontal and 6 vertical steps.
The number of ways in which these steps can be taken is given by,
[11! /(5! *6!)] = 462.
Answer: Option C
Answer: (C) 462
Question: Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 30 grades are D's. What is the number of students in the course?
(A)  80
(B)  110
(C)  160
(D)  600
(E)  400
Rationale: We start by creating a variable for the total number of students in the math course. We can say:
T = Total number of students in the math course
Next, we can use variable T in an equation that we translate from the given information. We are given that, of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 30 grades are D's. Since this represents all the grades in the class, it represents all the students in the class. Thus we know:
#A’s + #B’s + #C’s + #D’s = Total number of students in the class
1/5(T) + ¼(T) + ½(T) + 30 = T
We can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have:
4T + 5T + 10T + 600 = 20T
19T + 600 = 20T
600 = T
There are a total of 600 students in the math class.
Answer is D.
Answer: (D)  600
Question: How many liters of water must be evaporated from 50 liters of a 2-percent sugar solution to get a 10-percent solution?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: 2% of a 50 liter solution is 1L which is 10% of the solution at the end.
The solution at the end must be 1 L.
We need to evaporate 40 liters.
The answer is D.
Answer: (D) 40
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
(A) 11%
(B) 82%
(C) 14%
(D) 12%
(E) 17%
Rationale: 100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
Answer:D
Answer: (D) 12%
Question: If the tens digit of positive integers j, y are 6, how many values of the tens digit of 2(j+y) can be there?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If the tens digit of positive integers j, y are 6, how many values of the tens digit of 2(j+y) can be there?
A. 2
B. 3
C. 4
D. 5
E. 6
-> If j=y=60, 2(j+y)=240 is derived. If j=y=69, 2(j+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
Answer: (C) 4
Question: The length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 230
(B) 244
(C) 245
(D) 255
(E) 236
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30 = 25/2 ==> 2(120 + X) = 750 ==> X = 255 m.
Answer: Option D
Answer: (D) 255
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
(A) 5%
(B) 8%
(C) 10%
(D) 12%
(E) 6%
Rationale: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36)
= Rs. (520 + 1080)
= Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =(80/1600x 100)% = 5%.
Answer is A.
Answer: (A) 5%
Question: How many plants will be there in a circular bed whose outer edge measure 31 cms, allowing 4 cm2 for each plant ?
(A) 19
(B) 750
(C) 24
(D) 120
(E) None of these
Rationale: Circumference of circular bed = 31 cm
Area of circular bed = (31)2â„4Ï€
Space for each plant = 4 cm2
âˆ´ Required number of plants
= (31)2â„4Ï€ Ã· 4 = 19.11 = 19(approx)
Answer A
Answer: (A) 19
Question: If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
(A) 100
(B) 110
(C) 121
(D) 132
(E) 143
Rationale: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)
Therefore, the product should have factors with a difference of 2.
143 = 11*13, so this is a possible value for the original expression.
The answer is E.
Answer: (E) 143
Question: If B and C are digits and 8BC is a 3-digit number that is divisible by 5, which of the following is a possible product of B and C?
(A) 1
(B) 2
(C) 5
(D) 7
(E) 14
Rationale: Try with the options -
A. If BC = 1 , both B and C must be 1
B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2 = 11 which is not divisible by 3
C. If BC = 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5 = 14 which is not divisible by 3
D. If BC = 6 , then we can have the following possibilities
i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3 = 13 which is not divisible by 3
ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6 = 15 which is divisible by 3
E. If BC = 14 , then either B or C must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7 = 17 which is not divisible by 5
Thus answer is (D)
Answer: (D) 7
Question: A prize pool for a competition is divided up so that the first place winner receives 50%, the second place 30%, and third place receives 20%. If the third place competitor receives 100 000 dollars, how much is the total prize pool in dollars?
(A) 500 000
(B) 1 000 000
(C) 2 000 000
(D) 5 000 000
(E) 250 000
Rationale: The ratio is 5:3:2. Since third place received 100 000 dollars, a part-to-whole ratio can be set up to figure out how much the total prize pool is.
5+3+2 = 10
10/2 = X/100 000
5*100 000 = X
500 000 = X
Answer: A)
Answer: (A) 500 000
Question: A tap can fill a tank in 6 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) 3 hrs 48 min
(B) 3 hrs 45 min
(C) 3 hrs 75 min
(D) 6 hrs 45 min
(E) 3 hrs 55 min
Rationale: Time taken by one tap to fill the tank = 3 hrs.
Part filled by the taps in 1 hour = 4 * 1/6 = 2/3
Remaining part = 1 - 1/2 = 1/2
2/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min
So, total time taken = 3 hrs 45 min.
Answer: B
Answer: (B) 3 hrs 45 min
Question: a contract was signed to complete a job in 30 days. after how many days can 5 men leave then so that the job can be completed in 35 days
(A) 30 days.
(B) 35 days.
(C) 45 days.
(D) 55 days.
(E) 65 days.
Rationale: If no of men used initially is x, then after (35-x) days 5 men can leave so that the job can be completed in 35 days.
ANSWER:B
Answer: (B) 35 days.
Question: 3^9+3^9+3^9=?
(A) a) 243^5
(B) b) 243^4
(C) c) 243^2
(D) d) 243^6
(E) e) 243^15
Rationale: The correct answer is C 243^2
Answer: (C) c) 243^2
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:
(A) 86
(B) 88
(C) 92
(D) 94
(E) 96
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86.
A
Answer: (A) 86