mathewhe/aqua_rat huggingface dataset:
Question: In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?
(A) 16 2/3 %
(B) 25 percent
(C) 33 1/3 %
(D) 50%
(E) 75%
Rationale: 1986; 2/3
1988; 1/2
% decrease = change/ original*100
2/3−1/2 / 2/3∗100
1/6∗3/2∗100=14∗100 =25
Answer: "B"
Answer: (B) 25 percent
Question: What will be the cost of house to decorate which area equal to 324 sq ft, if the price per foot of building is Rs. 10?
(A) 120
(B) 240
(C) 360
(D) 720
(E) 860
Rationale: Let the side of the square plot be a ft.
a2 = 324 => a = 18
Length of the fence = Perimeter of the plot = 4a = 72 ft.
Cost of building the fence = 72 * 10
= Rs.720.
Answer: D
Answer: (D) 720
Question: In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?
(A) 20 min
(B) 15 min
(C) 10 min
(D) 5 min
(E) None of these
Rationale: Explanation :
The ratios of the speed of the fastest and the slowest is 2 : 1. Hence, they should meet only at one point at the circumference i.e the starting point (As the difference in the ratios in reduced form is 1).
For the two of them to meet for the first time, the faster shuld have completed one complete round over the slower one. Since, the two of them meet for the first time after 5 min, the faster one should have completed 2 rounds (i.e 2000 m) and the slower one should have completed 1 round (1000 in this time).
Thus the faster one would complete the race ( i.e 4000 m) in 10 min.
Answer : C
Answer: (C) 10 min
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 54, what is the total amount?
(A) 166
(B) 105
(C) 178
(D) 177
(E) 210
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 54
35 --- ? => 210
Answer: E
Answer: (E) 210
Question: Two pipes A and B can fill a cistern in 15 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/4 min
(B) 28 1/7 min
(C) 17 1/7 min
(D) 13 3/7 min
(E) 17 5/7 min
Rationale: 1/15 + 1/30 - 1/40 = 9/120
120/9 = 13 3/7
Answer:D
Answer: (D) 13 3/7 min
Question: A can do a job in 18 days and B can do it in 30 days. In how many days will they finish it together?
(A) 1/9
(B) 4/45
(C) 2/7
(D) 6/3
(E) 5/2
Rationale: Explanation:
1/18 + 1/30 = 8/90 = 4/45
So, both together will finish the work in 4/45 days.
Answer:B
Answer: (B) 4/45
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 4 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
(A) 5,500,000
(B) 2,400,000
(C) 55,000
(D) 28,000
(E) 280
Rationale: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 4 gms
In 400,000 cm^3 , X = 4 * 400,000 = 1,600,000 grams
In 1 cm^3, Y is 3 gms
In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms
Total gms in 1 m^3 = 1,600,000 + 1,800,000 = 2,400,000
ANSWER:B
Answer: (B) 2,400,000
Question: In the fifth grade at Parkway elementary school there are 470 students. 300 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 69.
(B) 135.
(C) 81.
(D) 91.
(E) 108.
Rationale: Total students = 470
Boys = 300, Girls = 170
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 170 - 35 = 135.
Correct option: B
Answer: (B) 135.
Question: Two negative numbers are multiplied to give a product of 48. If the lesser number is 10 less than thrice the greater number, what is the greater number?
(A) -6
(B) -8
(C) -5
(D) -9
(E) -10
Rationale: Test the options. The options give you the greater number.
(A) - 6
Triple of -6 is -18 and 10 less is -8.
-8 * -6 =48 (Correct)
Correct
Answer (A)
Answer: (A) -6
Question: A and B invests Rs.2500 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 11:5
(B) 15:16
(C) 15:2
(D) 9:9
(E) 11:1
Rationale: (2.5*6 + 5*6): (4*12)
45:48 =>
15:16
Answer:B
Answer: (B) 15:16
Question: A number is said to be prime saturated if the product of all the different positive prime factors of e is less than the square root of e. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95
Rationale: e=96 = 3 * 32 = 3 * 2^5
Answer is D.
Answer: (D) 96
Question: A can finish a work in 18 days and B can do the same work in 15 days. B
worked for 10 days and left the job. In how many days A alone can finish the
remaining work?
(A) 5
(B) 6
(C) 3
(D) 2
(E) 1
Rationale: B's 10 day's work=10/15=2/3
Remaining work=(1-(2/3))=1/3
Now, 1/18 work is done by A in 1 day.
Therefore 1/3 work is done by A in 18*(1/3)=6 days.
ANSWER B
Answer: (B) 6
Question: A basket has 4 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is
(A) 19/70
(B) 17/70
(C) 21/70
(D) 23/70
(E) 25/71
Rationale: Total fruits = 8Since there must be at least 3 apples,(4C3 * 4C1)/8C4 + 4C4/8C4 = 17/70.Answer:B
Answer: (B) 17/70
Question: When positive integer X is divided by positive integer Y, the remainder is 8. If X/Y = 96.12, what is the value of Y?
(A) 96
(B) 75
(C) 66.7
(D) 25
(E) 12
Rationale: When positive integer x is divided by positive integer y, the remainder is 8 --> x=qy+8;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=8 --> y=66.7.
Answer: C.
Answer: (C) 66.7
Question: John got a monthly raise of $237. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
(A) 327
(B) 723
(C) 732
(D) 231
(E) 237
Rationale: Let the 1st paycheck be x (integer).
John got a monthly raise of $ 237.
So after completing the 1st month he will get $ (x+237).
Similarly after completing the 2nd month she will get $ (x + 237) + $ 237.
= $ (x + 237 + 237)
= $ (x + 474)
So in this way end of every month his salary will increase by (E)$ 237.
Answer: (E) 237
Question: Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
(A) 52
(B) 67
(C) 71
(D) 73
(E) 79
Rationale: a+b= 6
b+c = 11
Refer England team: a+b+ (persons who only went to England) = 26
Persons who only went to England = 26 - (a+b) = 26-6 = 20
Refer French team: b+c+(persons who only went to France) = 26
Persons who only went to France = 26 - (b+c) = 15
Refer Italian team: a+b+c+f = 32
Now with above info.
Members of the club traveled to at least one of these three countries = Nothing but summation of all values (take only once)
Leftmost circle (England) : (20+a+b)
French: 15+c (all remaining already covered in previous circle)
Italy: f (all other variables taken in previous two circles)
(20+a+b)+(15+c)+f will give the answer
20+15+ a+b+c+f = 35+32 = 67
B is the answer.
Answer: (B) 67
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
(A) 20
(B) 22
(C) 23
(D) 26
(E) 30
Rationale: 36, 34, 30, 28, 24, ...
22 is next number.
ANSWER:B
Answer: (B) 22
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
(A) 641
(B) 640
(C) 188
(D) 177
(E) 166
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer:B
Answer: (B) 640
Question: 1, 9, 17, 33, 49, 73, ?
(A) 89
(B) 69
(C) 97
(D) 88
(E) 60
Rationale: C
97
The pattern is + 8, + 8, + 16, + 24,...
Answer: (C) 97
Question: To create paint with a certain shade of gray, one must combine 2.5 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
(A) 145.0
(B) 140.0
(C) 347.1
(D) 694.4
(E) 705.6
Rationale: Since the ratio of Black to White is 2.5 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.5:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. A is more than half so can not be the answer, B fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: (B) 140.0
Question: Which of the following fractions is greater than 1/4 and less than 3/5?
1. 3/4 2. 2/5 3. 1/2 4. 4/5 5. 1/5 6. 9/10
(A) 4/7
(B) 1/5
(C) 2/3
(D) 1/8
(E) 1/4
Rationale: 1/4 = 0.25, 3/5 = 0.6, 1/5= 0.2, 2/3= 0.66, 4/7=0 .57,1/8= 0.125.
Clearly, 0.57 lies between 0.25 and 0.60
Therefore, 4/7 lies between 1/4 and 3/5.
Answer is A.
Answer: (A) 4/7
Question: A train 700 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 277 m
(B) 700 m
(C) 600 m
(D) 187 m
(E) 1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (700 + x)/60 = 65/3
x =600 m.
Answer:C
Answer: (C) 600 m
Question: P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?
(A) 7 days
(B) 8 days
(C) 13
(D) 5 days
(E) 2days
Rationale: Explanation :
Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
=> q = 100/(23×130) = 10/(23×13)
Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13
=> P and Q together can do the work in 13 days
ANSWER:C
Answer: (C) 13
Question: Find the length of the wire required to go 10 times round a square field containing 53824 m2.
(A) 15840
(B) 9280
(C) 2667
(D) 8766
(E) 66711
Rationale: a2 = 53824 => a = 232
4a = 928
928 * 10 = 9280
Answer: B
Answer: (B) 9280
Question: In each term of a sequence, 7 is added to get the next term. If the first term is 3, what is the thirty-seventh term?
(A)  222
(B)  284
(C)  252
(D)  263
(E)  255
Rationale: 1rst term + 36 terms = 3 + 7+7+7+7+7+7+7+...+7 (36 times)
3 + (7 x 36) = 3 + 252 = 255
Answer E
Answer: (E)  255
Question: In a locality there are ten houses in a row. On a particular night a thief planned to steal from three houses of locality. In how many ways can he plan such that no two houses are next to each other?
(A) 56
(B) 73
(C) 80
(D) 100
(E) 120
Rationale: Lets say we have removed the three said houses. Now we are left with 7 houses.
If we arrange these 7 houses we have 8 places to put the other 3 houses at.
_ H1 _ H2 _ H3 _ H4 _ H5 _ H6 _ H7 _
so 8C3 = 56
ANSWER:A
Answer: (A) 56
Question: Sandy is younger than Molly by 12 years. If the ratio of their ages is 7:9, how old is Sandy?
(A) 42
(B) 49
(C) 56
(D) 63
(E) 70
Rationale: Let Sandy's age be 7x and let Molly's age be 9x.
9x - 7x = 12
x = 6
Sandy is 42 years old.
The answer is A.
Answer: (A) 42
Question: In how many different number of ways a Committee of 2person of can be selected from 2boys and 2girls such that at least 1 girl is included in the committe
(A) 3
(B) 4
(C) 2
(D) 5
(E) 9
Rationale: 1G 1B 2G
= (2C1*2C1)+2C2
= (2*2)+1
= 5
Total 2M 2W
4C2=6
2C2=1
At least one girl = total - with out girl
At least one girl = 6-1=5
D)
Answer: (D) 5
Question: If n is a natural number, then 6n^2 + 6n is always divisible by?
(A) 6 only
(B) 6 and 12
(C) 12 only
(D) 18 only
(E) 20 only
Rationale: 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B
Answer: (B) 6 and 12
Question: A board 5ft. 2 inches long is divided into 3 equal parts . What is the length of each part?
(A) 5ft. 7 inches
(B) 3ft. 7 inches
(C) 4ft. 7 inches
(D) 1ft. 8.7 inches
(E) 1ft. 7 inches
Rationale: Length of board=5ft. 2 inches=(5*12+2)inches=62 inches.
Therefore, Length of each part = (62/3) inches = 20.7 inches = 1ft. 8.7 inches
Answer is D.
Answer: (D) 1ft. 8.7 inches
Question: A train is moving at a speed of 50km/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) 36sec
(D) 29sec
(E) 52sec
Rationale: Speed of the train = 50*5/18 = 250/18 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(250/18) = 500*18/250 = 36sec
Answer is C
Answer: (C) 36sec
Question: William is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be Coconut oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If William accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be Coconut oil?
(A) 15/29
(B) 5/8
(C) 5/16
(D) 1/2
(E) 13/27
Rationale: Coconut oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;
If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are Coconut oil --> proportion = 15/29.
Answer: A.
Answer: (A) 15/29
Question: A third of Arun’s marks in mathematics exeeds a half of his marks in english by 80.if he got 240 marks In two subjects together how many marks did he got inh english?
(A) 120,60
(B) 180,60
(C) 180,90
(D) 120,40
(E) None of them
Rationale: Let Arun’s marks in mathematics and english be x and y
Then 1/3x-1/2y=30
2x-3y=180……>(1)
x+y=240…….>(2)
solving (1) and (2)
x=180
and y=60
Answer is B.
Answer: (B) 180,60
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $400 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
(A) 3000
(B) 5000
(C) 2000
(D) 4000
(E) 6000
Rationale: So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $200, thus 0.2x = $200 --> x = $1,000.
Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,000 = $2,000.
Answer:C
Answer: (C) 2000
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) 589
(B) 580
(C) 585
(D) 582
(E) 523
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer:C
Answer: (C) 585
Question: A train 105 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) 22
(B) 50
(C) 42.8
(D) 288
(E) 12
Rationale: Speed of the train relative to man = (105/10) m/sec = (21/2) m/sec. [(21/2) * (18/5)] km/hr = 37.8 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 37.8 ==> x = 42.8 km/hr.Answer: C
Answer: (C) 42.8
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/21
(B) 5/28
(C) 5/22
(D) 5/23
(E) 5/20
Rationale: Explanation:
Number of ways of (selecting at least two couples among five people selected) =
As remaining person can be any one among three couples left.
Required probability =
= (10 * 6)/252 = 5/21
Answer: A
Answer: (A) 5/21
Question: If A,B,C,D,E,F,G,H,I,J are in an increasing Arithmetic Progression as such. Then Which of the following operations will result in both mean and the median being modified.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed
(A) 1) A and E
(B) 2) A and D
(C) 3) A,C,D
(D) 4) All of them
(E) 5) None of them
Rationale: Here answer will be (A).
There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. Only options that remove a digit or digits from one side of the middle two numbers will result in change of mean and median.
Answer: (A) 1) A and E
Question: In a certain town, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 360 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
(A) 96
(B) 108
(C) 120
(D) 132
(E) 140
Rationale: The ratio of Yankees:Mets:Red Sox = 6:4:5
The Mets fans are 4/15 of the population.
(4/15)*360 = 96
The answer is A.
Answer: (A) 96
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120 cm2
(B) 765 cm2
(C) 216 cm2
(D) 197 cm2
(E) 275 cm2
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle
= 1/2 * 24 * 10
= 120 cm2
Answer: A
Answer: (A) 120 cm2
Question: In a kilometer race, A beats B by 80 meters or 10 seconds. What time does A take to complete the race?
(A) 180 sec
(B) 190 sec
(C) 115 sec
(D) 490 sec
(E) 390 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/80
= 125 sec.
Time taken by A = 125 - 10
= 115 sec.
Answer:C
Answer: (C) 115 sec
Question: There are 30 socks in a drawer. Sixty percent of the socks are red, and the rest are blue. What`s the minimum number of socks that must be taken from the drawer without looking in order to be certain that at least 2 blue socks have been chosen?
(A) - 2
(B) - 3
(C) - 14
(D) - 19
(E) - 20
Rationale: This is actually not a probability problem. Instead, it is an optimization problem, a minor type of question on GMAT.
Your first step is to calculate 60% of 30, which yields 18. Now, you must be sure you picked at least 2 blue socks. The only way is to pick all the other socks plus 2 blue socks. In this case, you would have to pick 18 red socks plus the 2 blue ones. Hence, answer is 20. If you had 4 green, 6 yellow and 8 red socks, the answer would be the same. You would have to pick all of those pluse 2 blue ones.answer is E
Answer: (E) - 20
Question: Find the average of all numbers between 3 and 69 which are divisible by 5
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60+65)/13=455/13=35
Answer: Option E
Answer: (E) 35
Question: The sum of two prime numbers is 85. What is the product of these two prime
numbers?
(A) 85
(B) 91
(C) 115
(D) 133
(E) 166
Rationale: Since there is only one even prime number (2), and the sum of two odd numbers is
even, the product of these two numbers must be even.
correct answer E
Answer: (E) 166
Question: The difference between simple interest and the compound interest on Rs.600 for 1 year at 10% per annum, reckoned half-yearly is :
(A) Nil
(B) Rs.6.60
(C) Rs.4.40
(D) Rs.1.50
(E) Cannot be determined
Rationale: Explanation:
S.I = Rs. (600×10×1/100) = Rs.60
C.I = Rs. [600×(1+5/100)2−600] = Rs.61.50
Difference = Rs.(61.50-60) = Rs.1.50
Correct Option: D
Answer: (D) Rs.1.50
Question: How many numbers from 10 to 1000 are exactly divisible by 9?
(A) 100
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: 10/9 = 1 and 1000/9 = 111 ==> 111 - 1 = 100. Therefore 100
Answer : A
Answer: (A) 100
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) 8000
(B) 9000
(C) 7000
(D) 10000
(E) 11000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
D
Answer: (D) 10000
Question: How many times the keys of a writer have to be pressed in order to write first 500 counting no's?
(A) 1372
(B) 1382
(C) 1392
(D) 1362
(E) 1352
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 500 = 401 * 3 = 1203
-----------
1392
C
Answer: (C) 1392
Question: In a certain sequence, the first term is 4, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
(A) 13/8
(B) 23/14
(C) 8/5
(D) 5/8
(E) 8/13
Rationale: let five terms in the sequence be a,b,c,d,e
a=4
b= 1+1/4=5/4
c=1+4/5= 9/5
d= 1+5/9 = 14/9
e= 1+9/14 = 23/14
hence answer should be B.
Answer: (B) 23/14
Question: Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 54, find the ages of Toby and Debby?
(A) 10 and 14
(B) 5 and 9
(C) 5 and 10
(D) 6 and 10
(E) 7 and 11
Rationale: Let the age of Debby be x and Toby be x-4
3 ( x + x-4 ) = 54
x = 11
The ages of Toby and Debby are 7 and 11.
Answer : E
Answer: (E) 7 and 11
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 11 inclusive?
(A) 420
(B) 840
(C) 1260
(D) 2520
(E) 27,720
Rationale: We have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, and 11.
The LCM is 1*2^3*3^2*5*7*11= 27,720
The answer is E.
Answer: (E) 27,720
Question: A tap can fill a tank in 10 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 1 hr 20 min
(B) 4 hr
(C) 3 hr
(D) 6 hr 40 min
(E) 2 hr 50 min
Rationale: Explanation:
1 tap can fill the tank in 10 hours.
Therefore
1 tap can fill half tank in 5 hours.
3 taps can fill the tank in 10/3 hour.
Therefore
3 taps can fill half tank in 10/6 hour =1 hour 40 minutes.
Total time taken=6 hour 40 minutes
Answer: Option D
Answer: (D) 6 hr 40 min
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 22 sec
(B) 89 sec
(C) 77 sec
(D) 99 sec
(E) 55 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer:B
Answer: (B) 89 sec
Question: John buys a bike for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, what is his gain percent?
(A) 5 5/9%
(B) 5 5/11%
(C) 6%
(D) 6 6/11%
(E) 6 7/13%
Rationale: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % = 300	x 100	%	= 5 5/11%
5500
Answer B
Answer: (B) 5 5/11%
Question: By selling 18 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 27
(B) 26
(C) 25
(D) 23
(E) 21
Rationale: 80% --- 18
120% --- ?
80/120 * 18 = 27
Answer:A
Answer: (A) 27
Question: If the speed of a man is 51 km per hour, then what is the distance traveled by him in 30 seconds ?
(A) 275m
(B) 360m
(C) 375 m
(D) 425 m
(E) 440 m
Rationale: The distance traveled in 30 sec = 51*(5/18) *30 =425m
ANSWER:D
Answer: (D) 425 m
Question: A work as fast as B. If B can complete a work in 16days independently,the number of days in which A and B can together finish the work in?
(A) 2days
(B) 3days
(C) 4days
(D) 5 1/3days
(E) 6days
Rationale: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/8
B's 1day work = 1/16
A+B 1day work = 1/8 + 1/16 = 3/16 => 16/3 = 5 1/3
A and B can finish the work in 5 1/3 days
Answer is D
Answer: (D) 5 1/3days