mathewhe/aqua_rat huggingface dataset:
Question: If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,
(A) 30
(B) 38
(C) 40
(D) 41
(E) 43
Rationale: Explanation:
Let daughter’s age = A and mother’s age = B
Given: 2A+B = 70 and A+2B = 95
Solving B, we will get B = 40. Answer: C
Answer: (C) 40
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of work. How long did the work last?
(A) 8 days
(B) 10 days
(C) 12 days
(D) 13 days
(E) 14 days
Rationale: Let the total units of work to be completed be 60.
Units of work completed by X in a single day = 60/20 = 3 units.
Units of work completed by Y in a single day = 60/12 = 5 units.
Thus, 8 units of work can be done by them in a single day working together.
X works for 4 days alone = 12 units of work.
Remaining work = (60 - 12) = 48 units.
Now, X and Y works together to complete the remaining work = 48/8 = 6 days
Hence, total days taken to complete the work = (6 + 4)= 10 days.
ANSWER:B
Answer: (B) 10 days
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?
(A) 22
(B) 27
(C) 19
(D) 37
(E) 21
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D
Answer: (D) 37
Question: The diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions?
(A) 140
(B) 150
(C) 289
(D) 330
(E) 390
Rationale: In revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm
Therefore, circumference of wheel = πd
= 22/7 × 21
= 66 cm
So, in 1 revolution distance covered = 66 cm
In 500 revolution distance covered = 66 × 500 cm
= 33000 cm
= 33000/100 m
= 330 m
ANSWER : D
Answer: (D) 330
Question: A committee of 3 men and 3 women must be formed from a group of 6 men and 8 women. How many such committees can we form if 1 man and 1 woman refuse to serve together?
(A) 610
(B) 710
(C) 810
(D) 910
(E) 1010
Rationale: The number of committees with John but not Mary:(1∗C52)(C73)=10∗35=350;
The number of committees with Mary but not John: (C53)(1∗C72)=10∗21=210;
The number of committees without John and without Mary: (C53)(C73)=10∗35=350.
Total = 350 + 350 + 210 = 910.
ANSWER:D
Answer: (D) 910
Question: The difference between the simple interest received from two different sources on Rs.1800 for 3 years is Rs.13.50. The difference between their rates of interest is
(A) 0.15%
(B) 0.25%
(C) 0.35%
(D) 0.45%
(E) 0.55%
Rationale: (1800xR1x3)/100-(100xR2x3)/100 =13.50
5400(R1-R2)=1350
R1-R2 = 1350/5400=0.25%
answer : B
Answer: (B) 0.25%
Question: In track last week, the boys ran twenty laps. The girls ran eight more laps. Each lap is a half of a mile. How many miles did the girls run?
(A) 10 miles
(B) 11 miles
(C) 12 miles
(D) 13 miles
(E) 14 miles
Rationale: The girls ran 20 + 8 = 28 laps. 28 x 1/2 = 28/2, which reduces to 14.
The girls ran 14 miles
correct answer E
Answer: (E) 14 miles
Question: A and B complete a work in 10 days. A alone can do it in 14 days. If both together can do the work in how many days?
(A) 5.8 days
(B) 4.78 days
(C) 6.25 days
(D) 3.15 days
(E) 2.75 days
Rationale: 1/10 + 1/14 = 6/35
35/6 = 5.8 days
Answer: A
Answer: (A) 5.8 days
Question: The sum of the mean, the median, and the range of the set {1, 2, 3,4,5} equals which one of the following values?
(A) 12
(B) 14
(C) 10
(D) 17
(E) 15
Rationale: set {1, 2, 3,4,5}
Mean = (1+2+3+4+5)/5 = 3
Meadian = Middle term = 3
Range = Highest - Lowest = 5-1 = 4
Mean+Median+Range = 3+3+4 = 10
Answer: Option C
Answer: (C) 10
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 277830, then population in 1978 was?
(A) 120000
(B) 228788
(C) 266891
(D) 240000
(E) 127791
Rationale: X * (105/100) * (105/100) * (105/100) = 277830
X = 277830/1.157625
X = 240000
Answer:D
Answer: (D) 240000
Question: Find the value of x which satisfies the relation
Log10 3+log10 (4x+1)=log10 (x+1)+1
(A) 2.5
(B) 3.5
(C) 3.2
(D) 6.8
(E) 9.8
Rationale: [log10a + log10b = log10 ab]
and also 1 can be written as log10 10,
so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)),
this can be solved to get 12x+3=10x+10,
that gives x=7/2=3.5
ANSWER:B
Answer: (B) 3.5
Question: The average of first six prime numbers which are between 20 and 60 is
(A) 34
(B) 42
(C) 45.7
(D) 57
(E) 67
Rationale: Explanation :
first six prime numbers which are between 20 and 60 = 23, 29, 31, 37, 41, 43
average = (23 + 29 + 31 + 37 + 41 + 43)/6
= 34
Answer : A
Answer: (A) 34
Question: 4 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 4 chairs. What is the likelihood that none of the 3 end up sitting in the same chair that they sat in during the first half?
(A) 3/24
(B) 9/24
(C) 15/24
(D) 1/8
(E) 21/24
Rationale: Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*1*1=3
and total possible outcomes =4!=24
probability of the favourable outcome= 1/8. D
Answer: (D) 1/8
Question: The simple interest on a sum of money will be Rs.500 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 2261
(B) 2888
(C) 1200
(D) 2699
(E) 900
Rationale: P --- 10 ---- 500
P --- 5 ----- 250
3P --- 5 ----- 750
------
=> 900
Answer: E
Answer: (E) 900
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
(A) Rs.2278
(B) Rs.2189
(C) Rs.2200
(D) Rs.2208
(E) Rs.2212
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs.2200
Answer: C
Answer: (C) Rs.2200
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
(A) 23/35
(B) 29/35
(C) 47/70
(D) 43/70
(E) None of these
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
ANSWER:A
Answer: (A) 23/35
Question: 3 men or 9 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 2 days
(B) 3 days
(C) 4 days
(D) 5 days
(E) 6 days
Rationale: 3M = 9W ---- 20 days
12M + 8W -----?
36W + 8 W = 44W ---?
9W ---- 20 44W -----?
9 * 20 = 44 * x => x = 4 days
ANSWER:C
Answer: (C) 4 days
Question: The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 50% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
(A) 18.75%
(B) 23%
(C) 15%
(D) 50%
(E) 100%
Rationale: Let wage of Erica = 10
Wage of Robin = 1.3*10 = 13
Wage of Charles = 1.5 *10 = 15
Percentage by which wage earned by Charles is more than that earned by Robin = (15-13)/13 * 100%
= 2/13 * 100%
=15%
Answer C
Answer: (C) 15%
Question: As x increases from 155 to 166, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)
(A)  I only
(B)  III only
(C)  I and II
(D)  I and III
(E)  II and III
Rationale: I. 2x - 5 --> x increases from 155 to 166 --> 2x increases --> 2x - 5 increases. Correct.
II. 1 - 1/x --> x increases from 155 to 166 --> 1/x decreases --> 1 -1/x increases. Correct.
III. 1/(x^2 - x) --> x increases from 155 to 166 --> x^2-x increases --> 1/(x^2 - x) decreases.
Answer: C.
Answer: (C)  I and II
Question: √7 percent of 7√7 =
(A) 0.55
(B) 0.96
(C) 0.1
(D) 0.45
(E) 0.6
Rationale: The other solutions are great, but here's one more approach.
First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION
All test-takers must memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
√6 ≈ 2.4
√7 ≈ 2.6
So, √7 percent of 7√7 ≈ 2.6 percent of (7)(2.6)
≈ (2.6/100)(18.2)
≈ 47.32/100
≈ 0.47
Check the answer choices to see that D is the only answer that's close.
Answer: D
Answer: (D) 0.45
Question: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 65 with him, what was the average amount with the group before his joining the group?
(A) s. 25.6
(B) s. 145/6
(C) s. 16.6
(D) s. 26
(E) s. 25
Rationale: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 50. So, the amount with remaining 6 people = 210 - 65 = Rs. 145
The average amount with them = 145/6
ANSWER:B
Answer: (B) s. 145/6
Question: A can complete a certain job in 18 days. B is 80% more efficient than A. In how many days can B complete the same job?
(A) 6
(B) 6.25
(C) 7
(D) 7.5
(E) 10
Rationale: Let, Total Work Unit = 180 Units
A can finish in 18 days = 180 unit work
i.e. A can finish in 1 days = 10 unit work
i.e. B can finish in 1 days = 10+(80/100)*10 = 18 unit work
Days in which B will complete the work alone = 180/18 = 10 days
Answer: Option E
Answer: (E) 10
Question: How many different ways can you select a pilot and a co pilot if you have 90 people to choose from?
(A) 199
(B) 200
(C) 398
(D) 4950
(E) 8010
Rationale: 90P2= 90!/(90-2)!=8010
E
Answer: (E) 8010
Question: Find the nearest to 25268 which is exactly divisible by 467?
(A) 1278
(B) 8100
(C) 1287
(D) 1771
(E) 1221
Rationale: Explanation:
900 * 3 * 3 = 8100
Answer: B
Answer: (B) 8100
Question: Amanda has had 3 pay cuts in her salary in the past 6 months. If the first pay cut was 12%, the second pay cut was 10% and the third was 10%. What will be the percentage decrease, if the salary is decreased in a single shot?
(A) 11.72%
(B) 38.72%
(C) 20.72%
(D) 18.72%
(E) 28.72%
Rationale: Let Rs.100 be initial salary.
Salary After 1st decrease, 12% = 88
Salary After 2nd decrease, 10% = 79.2 i.e. reduced by 10 percent of 88
Salary After 3rd decrease, 10% = 71.28 i.e. reduced by 10 percent of 79.2
So if its decreased in single shot =
i = ( ( b - a ) /b ) * 100
=28.72%
ANSWER:E
Answer: (E) 28.72%
Question: BOQD : ERTG :: ANPC : ?
(A) DQSF
(B) FSHU
(C) SHFU
(D) DSQF
(E) DSQU
Rationale: BOQD : ERTG::ANPC:DQSF
B-E:+3 A-D:+3
O-R:+3 N-Q:+3
Q-T:+3 P-S:+3
D-G:+3 C-F:+3
ANSWER:A
Answer: (A) DQSF
Question: A 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 288
(B) 300
(C) 889
(D) 276
(E) 234
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/36 = 50/3
3x + 900 = 1800 => x = 300 m.
Answer:B
Answer: (B) 300
Question: A man can swim in still water at 4 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.9
(C) 1.1
(D) 1.5
(E) 0.75
Rationale: M = 4
S = x
DS = 4 + x
US = 4 + x
4 + x = (4 - x)2
4 + x = 8 -2x
3x = 4
x = 0.75
Answer:E
Answer: (E) 0.75
Question: The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?
(A) 209%
(B) 200%
(C) 290%
(D) 600%
(E) 100%
Rationale: Explanation:
Let the salaries of A, B, C be x, 2x and 3x respectively.
Then,2x + 3x = 6000 => x = 1200.
A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600.
Excess of C's salary over A's=[ (2400 /1200) x 100] = 200%.
Answer: B) 200%
Answer: (B) 200%
Question: A train consists of 48 boxcars pulled by 2 engines. The boxcars are 15 meters long and the two engines are each 20 meters long. It crosses over a highway 24 meters wide at a speed of 14 m/s. How long does it take for the entire train to cross?
(A) 56 sec
(B) 63 sec
(C) 72 sec
(D) 81 sec
(E) 88 sec
Rationale: A
56 sec
d = 48 * 15 m + 2 * 20 m + 24 m= 784 m
T = 784 m / 14 m/s = 56 s
Answer: (A) 56 sec
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?
(A) 36
(B) 34
(C) 40
(D) 42
(E) 48
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 7
7[2x + 10] = 5[3x + 10]
14x + 70 = 15x + 50
15x - 14x = 70 - 50
x = 20
Then the first number is = 2
2x = 40
Short cut method:
a:b = 2:3
c:d = 5:7
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 7 ~ 3 * 5 = 14 ~ 15 = 1
2. If 10 is added both the number means 10 * 5 = 50 and 10 * 7 = 70,
Then 50 ~ 70 = 20
===> 1 -----> 20
===> 2 -----> 40 (Answer is = 40)
C
Answer: (C) 40
Question: A cyclist covers a distnce of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
(A) 28 km/hr
(B) 18 km/hr
(C) 20 km/hr
(D) 22 km/hr
(E) 24 km/h4
Rationale: Speed = { 750 } m/sec =5 m/sec = { 5 * 18 } km/hr =18km/hr
Option B
Answer: (B) 18 km/hr
Question: A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number J of imported lamps stocked at the store?
(A) 3
(B) 10
(C) 13
(D) 20
(E) 23
Rationale: We want to minimize not maximize the expression,.
J=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
But i'm guessing 123-5x/20 can be written as 123- x/4
if x has to be the greatest multiple of 4 less then 410, then it would be 408.
Hence 123-408/4 --> 123-102 -->21
Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E
Answer: (E) 23
Question: A certain car can travel 40 minutes on a gallon of gasoline at 80 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 80 mph?
(A) 15%
(B) 16%
(C) 25%
(D) 30%
(E) 40%
Rationale: Total time for travelling 80 miles @ 60 mph = 80/80 = 1 hour = 60 minutes.
Given, the car uses 1 gallon for every 40 minutes of driving @ 80 mph. Thus in 60 minutes it will use = 1.5 gallons. Thus, full tank = 1.5+8 = 9.5 gallons ---> 1.5/9.5= 16% of the fuel used. B is the correct answer.
Answer: (B) 16%
Question: A sum fetched a total simple interest of $4196.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(A) $8829
(B) $2840
(C) $6578
(D) $7782
(E) $8929
Rationale: E
8929
Principal
= $100 x 4196.25/9 x 5
= $419625/45
= $8929.
Answer: (E) $8929
Question: The sides of a rectangular region measured to the nearest centimeter are 8 cm and 7 cm. Out of the following which is the largest possible value of actual area of rectangle ?
(A) 48
(B) 55.25
(C) 52.29
(D) 44
(E) 61.07
Rationale: acan be anywhere between 7.5 and 8.4 andbcan be anywhere between 6.5 and 7.4.
Hence max area can be 8.4*7.4 eq 62.16.
largest value which is near to 62.16 is 61.07.
Hence E.
Answer: (E) 61.07
Question: A tradesman sold an article at a loss of 10%. If the selling price had been increased by $50, there would have been a gain of 10%. What was the cost price of the article ?
(A) $150
(B) $200
(C) $250
(D) $120
(E) $100
Rationale: Let C.P. be $x
Then 110% of x - 90% of x = 50
20% of x = 50
x/5 = 50
x = 250
Answer is C
Answer: (C) $250
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
(A) 6 hrs
(B) 10 hrs
(C) 15 hrs
(D) 30 hrs
(E) 25 hrs
Rationale: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15
ANSWER:C
Answer: (C) 15 hrs
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) 22%
(B) 15%
(C) 19%
(D) 12%
(E) 10%
Rationale: 100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
Answer:D
Answer: (D) 12%
Question: Which of the following is a parallelogram?
(A) 115,65,115,65(angle in deg)
(B) 120,30,130,20(angle in deg)
(C) 80,80,80,80(angle in deg)
(D) a & c
(E) none
Rationale: sum of adjacent angles is 180 degrees.
ANSWER:A
Answer: (A) 115,65,115,65(angle in deg)
Question: What is the shortest distance between points (-2, 1) and (2,-2)?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The shortest distance between any two points is a line.
Points are written in the (x,y) format, where x is the x-coordinate and y is the y-coordinate.
Calculate the difference between the x and y values of each coordinate.
Difference between y values = 1 - (-2) = 1 + 2 = 3
Difference between x values = (-2) - 2 = -4
If you start at (2, -2) and travel over -4 units (i.e., travel to the left) and then travel straight up 3 units, you will end up at (-2, 1). This sketches out a right triangle, where the hypotenuse is the length of the shortest distance between the two points (i.e., a straight line between the two points).
Use the Pythagorean Theorem with a = -4 and b = 3 to solve for this distance between the two points.
a2+ b2 = c2
(-4)2+ 32 = c2
Solve for c
16 + 9 = c2
25 = c2
c = 5 (Negative 5 cannot be a solution to a length so it is discarded)
Answer is E
Answer: (E) 5
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.883. Find the cost of each ice-cream cup?
(A) 25
(B) 76
(C) 29
(D) 12
(E) 20
Rationale: Explanation:
Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 883
96 + 225 + 490 + 6x = 883
6x = 72 => x = 12.
Answer:D
Answer: (D) 12
Question: If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions T represents the final price of the item?
(A) T=(10,000z + 100z(x – y) – xyz)/10,000
(B) T=(10,000z + 100z(y – x) – xyz)/10,000
(C) T=(100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: -A-
z=Original Price
x=MU
y=MD
New price with MU:
z (x/100+1)
New price with MD:
z[(x/100+1)(-y/100+1)]
Solvingâ€¦
=z[((x+100)/100)((-y+100)/100)]
=z(x100-xy+10000-100y)/10000
=(zx100-xyz+10000z-100yz)/10000 --> similar to A
Answer: (A) T=(10,000z + 100z(x – y) – xyz)/10,000
Question: How many three-digit integers between 313 and 401, exclusive, are divisible by 3 when the tens digit and the hundered digit are switched?
(A) 3
(B) 30
(C) 22
(D) 29
(E) 90
Rationale: Answer is 30
No of digits between 310 and 400 (exclusive) = 401-313-1 = 88
No Intergers divisble by 3 =~ 88/3 ~ 30
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.
e.g 372 is divisble by 3 (becae 3+7+2= 12 (divisble by 3))
switch digits 732 also divisble by 3 (becae 7+3+2= 12 (divisble by 3))
Divsiblivity rule for 3 is Sum of all digits must be divisble by 3. It doesn't matter if hundred digit and tens digits are switched.
You have right. So it is enough to proceed like usual to find the numbers in a given range that are divisible by 3. So 399-312/3 +1 =30.
Answer : B
Answer: (B) 30
Question: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $10 more than that received by B, find the total amount shared by A, B and C.
(A) $260
(B) $360
(C) $160
(D) $460
(E) $560
Rationale: A = 1/3 (B+C) => C = 3A - B ---(1)
B = 2/7 (A+C) => C = 3.5 B - A --(B)
A-B = $10
A = 10+B
(1)===> C = 30+3B - B = 2B+30 ==> 2B-C = -30 ---(3)
(2)===> C = 3.5 B - B-10 = 2.5B-10==>2.5B-C = 10---(4)
from (4) and (3) 0.5B = 40
B = $80
A= $90
C =270-80=$190 Total amount = 90+80+190 = $360
Answer: B
Answer: (B) $360
Question: A sum of money place at compound interest doubles itself in 5 years. In how many years will it amount to eight times itself?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: 100 ---- 200 ---- 5
400 ---- 5
800 ---- 5
------
15 years
Answer: D
Answer: (D) 15
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages?
(A) 16, 26, 36
(B) 16, 28, 36
(C) 16, 28, 38
(D) 16, 28, 32
(E) 16, 28, 30
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80 => x = 4
Their present ages are 16, 28 and 36 years respectively.
Answer: B
Answer: (B) 16, 28, 36
Question: During a certain two-week period, 75 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 2/3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
(A) 5 A
(B) 10 A
(C) 15 A
(D) 18 A
(E) 25 A
Rationale: Movies: 75 % comedies. 25 % remaining genre.
Now in this 25 %, there are only 2 categories. Action movies and Drama Movies.
If Action = x; Drama movies = 2x/3. Total 5x/3.
5x/3 = 25; x = 15
Action movies: 15 %
Drama movies: 10 %
we can say that out of 100 z,:
comedies: 75 z
action: 15 z
drama: 10 z
Now action movies were A
This means:
A = 15 z.
z = A/ 15
Comedies: 75 z = 75 * (A/15)
5 A
A is the answer.
Answer: (A) 5 A
Question: The average of Pratyush's marks in 7 subjects is 75. His average in six subjects excluding Science is 72. How many marks did he get in Science?
(A) 72
(B) 93
(C) 99
(D) 100
(E) 56
Rationale: Explanation :
Marks in Science (7*75 - 6*72) = 93.
Answer : B
Answer: (B) 93
Question: a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets) ?
(A) 3
(B) 4
(C) 5
(D) 2
(E) 1
Rationale: Explanation :
Exactly one of ab, bc and ca is odd⇒ Two are odd and one is evenabc is a multiple of 4⇒ the even number is a multiple of 4The arithmetic mean of a and b is an integer⇒ a and b are oddand so is the arithmetic mean of a, b and c.⇒ a+ b + c is a multiple of 3c can be 4 or 8.c = 4; a, b can be 3, 5 or 5, 9c = 8; a, b can be 3, 7 or 7, 9Four triplets are possible
Answer : B
Answer: (B) 4
Question: 1397 x 1397 = ?
(A) 1948609
(B) 1949609
(C) 1950609
(D) 1950709
(E) 1951609
Rationale: 1397 x 1397	= (1397)2
= (1400 - 3)2
= (1400)2 + (3)2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
E)
Answer: (E) 1951609
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets W did Irwin score?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored W=2 11-point baskets in my opinion.
Answer C
Answer: (C) 2