mathewhe/aqua_rat huggingface dataset:
Question: The sale price of a trolley bag including the sale tax is Rs. 1120. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
(A) Rs 1000
(B) Rs 1515
(C) Rs 800
(D) Rs 900
(E) None of these
Rationale: Explanation :
112% of S.P. = 1120
S.P. = Rs.(1120x 100/112) = Rs.1000.
C.P. = Rs (100/125x 1000) = Rs 800.
Answer : C
Answer: (C) Rs 800
Question: The ages of two person , differ by 20 years. If 5 years ag , the elder one be 5 times as old as the younger one their present ages (in years) are respectively
(A) 30, 10
(B) 20,10
(C) 35,15
(D) 51,17
(E) 20,17
Rationale: Let their ages be x and (x + 20) years
(x - 5) * 5 = (x +20 - 5)
after solving this we get
x= 10 years
The age of elder one = 10 + 20 = 30 years
So the present ages are 30 and 10 years
ANSWER : A
Answer: (A) 30, 10
Question: A van takes 5 hours to cover a distance of 495 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time?
(A) 60
(B) 63
(C) 66
(D) 69
(E) 72
Rationale: (3/2)*5 = 7.5 hours
495 / 7.5 = 66 kph
The answer is C.
Answer: (C) 66
Question: SP of a book is Rs. 450 he gets a loss of 10%, find CP of the book?
(A) Rs.300
(B) Rs.450
(C) Rs.500
(D) Rs.600
(E) Rs.640
Rationale: Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Rs.500
C
Answer: (C) Rs.500
Question: Complete the sequence:
E G K Q ?
(A) M
(B) D
(C) Y
(D) F
(E) Z
Rationale: E+2=G
G+4=K
K+6=Q
Q+8=Y
C
Answer: (C) Y
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is y + 2?
(A) y - 3
(B) y-57
(C) y - 1
(D) y
(E) x + 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= y+2
n= y+1
1st integer= y+1-4= y-3
A is the answer
Answer: (A) y - 3
Question: Right triangle PQR is the base of the prism in the figure above. If PQ=PR=âˆš14 and the height of the prism is 8, what is the volume of the prism?
(A) 12
(B) 45
(C) 87
(D) 56
(E) 23
Rationale: Volume of prism = Area of base * height = 1/2* (square root of 14) * (square root of 14)*8 =56
Answer: D
Answer: (D) 56
Question: Two pipes P and Q can fill a cistern in 12 and 16 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/2 min
(B) 11 1/4 min
(C) 11 2/4 min
(D) 12 min
(E) 11 7/4 min
Rationale: 3/12 + x/16 = 1
x= 12
Answer: D
Answer: (D) 12 min
Question: The total of the ages of Amar, Akbar and Anthony is 30 years. What was the total of their ages three years ago ?
(A) 20 years
(B) 28 years
(C) 71 years
(D) 21 years
(E) 31 years
Rationale: Explanation:
Required sum = (30 - 3 x 3) years = (30 - 9) years = 21 years.
Answer: Option D
Answer: (D) 21 years
Question: At a certain college, 80 percent of the total number of students are freshmen. If 60 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 50 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
(A) 25%
(B) 20%
(C) 22%
(D) 21%
(E) 24%
Rationale: Let's say there is a TOTAL of100students at this college.
80 percent of the total number of students are freshmen.
# of freshmen = 80% of 100 =80
60 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 60% of 80 = 48
...and, of these, 50 percent are psychology majors...
Number of liberal arts freshmen who are psychology majors = 50% of 48=24
What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
24/100= 24%
Answer:E
Answer: (E) 24%
Question: The salaries of a,b,c are in the ratio 2:3:5.If the increment of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
(A) 23:33:60
(B) 24:33:60
(C) 23:33:66
(D) 23:38:60
(E) 28:33:60
Rationale: a:b:c = 2 :3 :5
200:300:500
15% 10% 20%
+30 +30 +100
230:330:600 = 23:33:60
ANSWER:A
Answer: (A) 23:33:60
Question: S=√[2√63 + 2/(8+3√7)] =
(A) 8 + 3√7
(B) 4 + 3√7
(C) 8
(D) 4
(E) √7
Rationale: In these type of question u multiply the nominator and denominator with conjugate...Conjugate of 8 +3sqrt(7) is 8 -3sqrt(7)
sqrt[2sqrt(63) + 2 { 8 - 3sqrt(7)}/{64 - 63}]
S=sqrt[2sqrt(63) +16 - 2sqrt(63)] =4
Answer is 4.D
Answer: (D) 4
Question: 6+2+2^2+2^3+2^4+2^5=？
(A) (2^3-1)(2^3+1)
(B) 2^5-1
(C) 2^6+4
(D) 2^5+1
(E) 2^5-2
Rationale: From 6+2+2^2+2^3+2^4+2^5=68,
2^6+4=68
the correct answer is C.
Answer: (C) 2^6+4
Question: The sum of the present ages of A, B, C is 45 yrs. Three years ago their ages were in the ratio 1:2:3. What
is the present age of A
(A) 10yrs
(B) 6yrs
(C) 8yrs
(D) 9yrs
(E) 7yrs
Rationale: a:b:c=1:2:3
a=1x;b=2x;c=3x;
after three years
(x+3)+(2x+3)+(3x+3)=45;
x=6;
so present age of a will be x+3=6+3=9
ANSWER:D
Answer: (D) 9yrs
Question: The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5808 sq cm. What is the ratio of the width and the area of the rectangle?
(A) 1:76
(B) 1:80
(C) 1:84
(D) 1:88
(E) 1:92
Rationale: Let the length and the width be 4x and 3x respectively.
Area = (4x)(3x) = 5808
12x^2 = 5808
x^2 = 484
x = 22
The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1 : 88
The answer is D.
Answer: (D) 1:88
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
(A) 31 minutes
(B) 37 minutes
(C) 32 minutes
(D) 30 minutes
(E) 33 minutes
Rationale: 30 minutes
Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer: (D) 30 minutes
Question: I bought a car with a peculiar 5 digit numbered licence plate which on reversing could still be read. On reversing value is increased by 78633.Whats the original number if all digits were different?
(A) 10968
(B) 10969
(C) 10868
(D) 11968
(E) 12968
Rationale: Only 0 1 6 8 and 9 can be read upside down. So on rearranging these digits we get the answer as 10968.
ANSWER:A
Answer: (A) 10968
Question: You cook a pot of beef stew for you and your roommate. Normally it lasts 7 days between the two of you. If 3 guests are now staying with you and your roommate, how many days will the beef stew now last if everyone eats it?
(A) 2.8
(B) 1
(C) 3.5
(D) 14
(E) 1.6
Rationale: First set up a ratio with all the relevant values and also the unknown variable:
2*7 = 5*x
Now solve by multiplying 2 by 7 and then dividing that product by 5:
2*7 = 14
14/5 = x
x = 2.8
The value of x represents the amount of days a bot of beef stew will last for 5 total people.
Answer: A
Answer: (A) 2.8
Question: a;b = 8: 10, b:c = 7: 9, a:b:c = ?
(A) 56 : 70: 80
(B) 56 : 70: 70
(C) 56 : 70: 60
(D) 56 : 70: 95
(E) 56 : 70: 90
Rationale: a;b = 8: 10
b:c = 7: 9
a:b:c =56 : 70: 90
Answer : E
Answer: (E) 56 : 70: 90
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
(A) 2999
(B) 2777
(C) 1000
(D) 297
(E) 2781
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer:C
Answer: (C) 1000
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 5
(B) 4
(C) 6
(D) 8
(E) 3
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%.Answer:B
Answer: (B) 4
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word GUAVA could be arranged to create a five-letter code?
(A) 5!
(B) 5! − (3! + 2!)
(C) 5! − 2!
(D) 5!/2!
(E) 6!/(3! × 2!)
Rationale: GUAVA - five letters can be arranged in 5! ways
since 'A' repeats 2 times , we need to divide the 5! ways by 2! to adjust repetition.
5!/(2!)
Ans. D) 5!/(2!)
Answer: (D) 5!/2!
Question: A sum of money place at compound interest doubles itself in 10 years. In how many years will it amount to eight times itself?
(A) 10 years
(B) 20 years
(C) 30 years
(D) 40 years
(E) 50 years
Rationale: 100 ---- 200 ---- 10
400 ---- 10
800 ---- 10
------
30 years
Answer: C
Answer: (C) 30 years
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(A) Rs. 3500
(B) Rs. 3750
(C) Rs. 3840
(D) Rs. 3900
(E) None
Rationale: EXPLANATION
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5b/2 x
15x + 2y = 4000
15x + 2 x 5/2 x= 4000
20x = 4000
x = 200.
So, y = 172 = 500.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
Answer D
Answer: (D) Rs. 3900
Question: The ratio between the number of sheep and the number of horses at the Stewart farm is 6 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
(A) 18
(B) 28
(C) 48
(D) 56
(E) 60
Rationale: Let the number of sheeps and horses be 4x and 7x.
Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8
Sheeps =6x = 6*8 = 48.
Hence C.
Answer: (C) 48
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 21
(C) 25
(D) 27
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.12000. A's share is?
(A) 2999
(B) 2778
(C) 6000
(D) 2889
(E) 4000
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 12000 = 4000
Answer:E
Answer: (E) 4000
Question: Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
(A) 7:7
(B) 7:4
(C) 7:1
(D) 7:6
(E) 7:8
Rationale: Let x be the investment of Ravi in 6% and y be in 7%
x(6)(n)/100 = y(7)(n)/100
=> x/y = 7/6
x : y = 7:6
Answer: D
Answer: (D) 7:6
Question: The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?
(A) 80 days
(B) 30 days
(C) 65 days
(D) 16 days
(E) 15 days
Rationale: one man can consume the same food in 30*40 = 1200 days.
10 more men join, the total number of men = 40
The number of days the food will last = 1200/40
= 30 days.
Answer:B
Answer: (B) 30 days
Question: The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?
(A) 25 years
(B) 30 years
(C) 36 years
(D) Cannot be determined
(E) None of these
Rationale: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.
Then, (1/3 * 5x)/(1/2 * 6x) = 5/9
15 = 15
Thus, Shaan's age cannot be determined.
ANSWER:D
Answer: (D) Cannot be determined
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) 1261
(B) 1268
(C) 1269
(D) 1265
(E) 1263
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer:A
Answer: (A) 1261
Question: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 38 percent ryegrass, what percent of the weight of this mixture is X ?
(A)  10%
(B)  33.33 %
(C)  40%
(D)  86.66%
(E)  66.66 %
Rationale: ---------------->Ryegrass
X-------------->	40%
Y-------------->	25%
M(mixture)---->38%
0.4X + (M-X)0.25 = 0.38M
0.15X = 0.13M
X = 0.8666M
X = 86.66% of M
D
Answer: (D)  86.66%
Question: A bag is filled with pennies and nickels in the ratio of 10 to 5. There are 60 nickles in the bag, how many coins are there in that bag?
(A) 40
(B) 180
(C) 65
(D) 70
(E) 80
Rationale: A ratio of pennies to nickels of10 to 5 means that we can write the number of pennies and nickels in the form
number of pennies = 10x and number of nickels = 5x
But we know the number of nickels, 60. Hence
5x = 60
Solve for x
x = 12
The total number of coins is given by
10x + 5x = 15x = 15 × 12 = 180
Answer : B
Answer: (B) 180
Question: ((469 + 174)2 - (469 - 174)2)/(469 x 174) = ?
(A) 2
(B) 4
(C) 295
(D) 643
(E) 653
Rationale: Given exp. = ((a + b)2 - (a - b)2)/ab
=4ab/ab
= 4
ANSWER:B
Answer: (B) 4
Question: A cheetah runs m miles in n hours. How many miles will it run in x hours at the same rate?
(A) mnx
(B) m⁄n
(C) mx⁄n
(D) mx
(E) mn⁄x
Rationale: Given Speed = m/n
To Find distance in x hours with same speed
Distance = speed * time
Distance = m/n*x = mx/n
Answer C
Answer: (C) mx⁄n
Question: A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree.
From the diagram, (36−x)2=x2+122(36−x)2=x2+122
⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144
⇒72x=1296−144⇒72x=1296−144
⇒x=16
Answer:A
Answer: (A) 16
Question: What percent of a day is 7 hours?
(A) 29.2%
(B) 12.5%
(C) 13%
(D) 11.3%
(E) None of these
Rationale: Explanation :
Solution: required percentage = (7/100 * 24) = 29.2%
Answer : A
Answer: (A) 29.2%
Question: A two digit number when 18 added becomes another two digit number with reversed digits. How many such two digit numbers are possible?
(A) 2
(B) 3
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
Let the two digit number be 'ab' and the number formed after adding 18 to it is 'ba'
So ab + 18 = ba
⇒⇒ (10a + b) + 18 = 10b + a
⇒⇒ 18 = 9b – 9a
⇒⇒ 2 = b – a
So we know that ab, ba both are two digit numbers so a, b ≠≠ 0.
Also when b = 9, a = 7; b = 8, a = 6; b = 7, a = 5; b = 6, a = 4; b = 5, a = 3; b = 4, a = 2; b = 3, a = 1
Total 7 combinations are possible.
Correct Option: C
Answer: (C) 7
Question: 78 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 13
(C) 26
(D) 15
(E) 16
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons	30	:	78	:: 12 : x
Working hours/day	6	:	5
30 x 6 x x = 78 x 5 x 12
x =	(78 x 5 x 12)/(30 x 6)
x = 26.
ANSWER:C
Answer: (C) 26
Question: For every $30 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
(A) 1 : 4 : 400
(B) 1 : 4 : 100
(C) 1:4:600
(D) 100 : 4 : 1
(E) 400 : 4 : 1
Rationale: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 150 dollar of B
therefore 4 dollar M = 600 dollar of B also 1 dollar Y
Y:M:B = 1:4:600
= 1:4:600
C
Answer: (C) 1:4:600
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 80?
(A) 24
(B) 26
(C) 20
(D) 22
(E) 18
Rationale: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 80
4n< 73
n < 18. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 18)
Combining the two
-1.5 < n<18.25
n = 1 to 18 (18 integers)
and n = -1 and 0
so 20 integers.
C is the answer
Answer: (C) 20
Question: Express of the following as a fraction:
42%
(A) 20/55
(B) 21/50
(C) 34/27
(D) 17/25
(E) None of them
Rationale: 42% = 42/100= 21/50.
Answer is B.
Answer: (B) 21/50
Question: Find out the C.I on Rs.3000 at 4% p.a. compound half-yearly for 1 1/2 years
(A) 183.62
(B) 106.07
(C) 106.04
(D) 106.03
(E) 186.01
Rationale: A = 3000(51/50)3
= 3183.62
3000
-----------
183.62
Answer:A
Answer: (A) 183.62
Question: A container holds 4 quarts of milk and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts milk to 5 parts water by volume?
(A) 4/3
(B) 5/3
(C) 7/3
(D) 8/3
(E) 10/3
Rationale: An alternate to the alligation method is the more direct/algebraic method:
Let x be the amount of water to be added.
New total amount of water = 4+x
Total amount of milk= 4
New total = 4+4+x=8+x
Final ratio required (for water) = 5/(5+3)=5/8
Thus, (4+x)/(8+x) = 5/8 --> solving for x you get x = 8/3.
D is thus the correct answer.
Answer: (D) 8/3
Question: A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?
(A) .1
(B) .2
(C) 3/10
(D) .4
(E) .5
Rationale: C (3,6) - all the possible arrangements
C(2,4) is the number of ways the committe with Tom and without Mary.
P = C(2,4)/(C 3,6) = 3/10 C
Answer: (C) 3/10
Question: At a certain conference, 22% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 60% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
(A)  18.0%
(B)  62.0%
(C)  79.2%
(D)  55.0%
(E)  82.0%
Rationale: Refer to the table in the attachment:
Let x= No. of members who have paid in Full
60 % members paid in full and did not register in advance = 0.6x
22 % registerd in advance and paid in full.
So if total No. of members = 100, then 22 members paid Full and registered in advance.
Hence total members who paid full amount = 0.6x + 22 =x
0.4x =22
Hence x = 55
i.e. 55 out of 100 or 55 %
Ans. D
Answer: (D)  55.0%
Question: Sometime after 10:00 PM a murder took place. A witness claimed that the clock must have stopped at the time of the shooting. It was later found that the postion of both the hands were the same but their positions had interchanged. Tell the time of the shooting (both actual and claimed).
(A) 10:59 PM
(B) 11:59 PM
(C) 10:50 PM
(D) 10:52 PM
(E) 10:55 PM
Rationale: Actual time of shooting = 11:54 PM
Claimed Time = 10:59 PM
ANSWER:A
Answer: (A) 10:59 PM
Question: The least number which must be subtracted from 670 to make it exactly divisible by 9 is:
(A) A)2
(B) B)3
(C) C)4
(D) D)5
(E) E)6
Rationale: On dividing 670 by 9, we get remainder= 4
Therefore, required number to be subtracted= 4
Answer: C
Answer: (C) C)4
Question: A is a positive integer. when a is divided by 4 the remainder is 3, and when divided by 9 the remainder is 1. what is the remainder if a is divided by 52?
(A) Between 1 and5, inclusive
(B) Between 10 and15, inclusive
(C) 5
(D) Between 8 and 12, inclusive
(E) Between 4 and 8, inclusive
Rationale: Given the integer a
4a+3= 9a+5
Start 4a+3 -->7, 11, 15,...59,....
Of these only 55 fit the description 9a+5. The remainder when divided by 52 is 7. So answer is E).
Answer = E)
Answer: (E) Between 4 and 8, inclusive
Question: If x and y are numbers such that (x+8)(y-8)=0, what is the smallest possible value of x^2 + y^2
(A) 4
(B) 24
(C) 54
(D) 64
(E) 94
Rationale: From (x+8)(y-8)=0 it follows that either, x=-8 or y=8. Thus either x^2=64 or y^2=64.
Now, if x^2=64, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 64 + 0 = 64.
Similarly if y^2=64, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 64 = 64.
Answer: D.
Answer: (D) 64
Question: An article is bought for Rs.690 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 8/3%
(C) 33 1/3%
(D) 30 10/23%
(E) 32 1/3%
Rationale: 690 ---- 210
100 ---- ? => 30 10/23%
Answer:D
Answer: (D) 30 10/23%
Question: In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2,or 3 is obtained. Mary played the game, getting at least one score of each of 1, 2, and 3, and never getting the same score in consecutive steps. What is the greatest possible score that Mary could have gotten?
(A) 7
(B) 8
(C) 5
(D) 9
(E) 5
Rationale: There are two conditions:
1. Mary got at least one score of each of 1, 2, and 3.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Angel could have gotten is 3 + 1 + 3 + 2 = 9.
Answer: D.
Answer: (D) 9
Question: A can do a work in 15 days and B in 20 days. If they work on it together then in how many days required to complete the work?
(A) 300/31
(B) 300/35
(C) 300/21
(D) 300/15
(E) 300/20
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 15 ) ( 20 ) (300/35)
Rate - ( 20 ) ( 15 ) ( 35 )
Work -(300) (300) (300)
therefore A+B requires (300/35) days to complete entire work
= 300/35
Answer is B
Answer: (B) 300/35
Question: Which of the following is closer to (4!+3!)-(4!-3!)?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: 4!+3!)-(4!-3!)=24+6-24+6
= 12
Answer: D
Answer: (D) 12
Question: If an examination 63% of the candidates in English,65% passed in Mathematics, and 27% failed in both subjects.What is the pass percentage?
(A) 55%
(B) 60%
(C) 65%
(D) 75%
(E) None.
Rationale: Fail in English=100-63=37%
Fail in maths=100-65=35%
so pass %= 100-(37+35-27)=55%
ANSWER:A
Answer: (A) 55%
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4991
(B) Rs. 5991
(C) Rs. 6001
(D) Rs. 6991
(E) None of these
Rationale: Explanation:
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
ANSWER IS A
Answer: (A) Rs. 4991
Question: A's 5th birthday is on 12th which is a (say) Monday of a leap year. What willbe the day on their 6th birthday?
(A) sunday
(B) monday
(C) tuesday
(D) wednesday
(E) thursday
Rationale: If 5th Birthday is on or before Feb 29, then 6th Birthday is on Wednesday.
If 5th Birthday is after Feb 29, then 6th Birthday is on Tuesday.
ANSWER:C
Answer: (C) tuesday
Question: A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 9 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
(A) 3
(B) 9
(C) 15
(D) 21
(E) 30
Rationale: Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.
Then under plan A the cost would be $0.6+0.06(t-9) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-9)=0.08t --> 60+6(t-9)=8t --> t=3.
Answer: A.
Answer: (A) 3
Question: Wayne goes to a fruits vendor to purchase mangoes and oranges. The cost of 4 mangoes is $10, and the cost of 5 oranges is $10. If Wayne buys fruits worth $31, he has purchased at least how many mangoes?
(A) 1
(B) 2
(C) 6
(D) 8
(E) 13
Rationale: Cost of each mango = $10 / 4 = $2.50.
Cost of each orange = $10 / 5 = $2.
Let number of mangoes be m, and number of oranges be o.
Then 2.5m + 2o = 31
=> 5m + 4o = 62
=> 5m = 62 - 4o
To find minimum m, we need to maximize o, and ensure that (62 - 4o) is divisible by 5.
o = 3, m = (62 - (4)3) / 5 = 10.
o = 8, m = (62 - (4)8) / 5 = 6.
o = 13, m = (62 - (4)13) / 5 = 2.
More than this, m will go -ve. So, Wayne has to purchase at least 2 mangoes.
Answer: B
Answer: (B) 2