mathewhe/aqua_rat huggingface dataset:
Question: If the mean of weight of students in a class of weight 38, 50, 70, 88 and 110 is 71.5 kg, what is the mean of the class if student of weight 50 kg left the class?
(A) 72 kg
(B) 75 kg
(C) 68.5 kg
(D) 76.5 kg
(E) 80.5 kg
Rationale: Mean = (Sum of all weights in class)/(no. students)
M1 = (38+70+88+110)/(4)
= 76.5 kg
Answer =D
Answer: (D) 76.5 kg
Question: If A speaks the truth 70% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
(A) 0.49
(B) 0.48
(C) 0.41
(D) 0.42
(E) 0.411
Rationale: Explanation:
Probability that A speaks truth is 70/100 = 0.7
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.7× 0.6 = 0.42
Answer: D
Answer: (D) 0.42
Question: Convert the following into a fraction:1.0%
(A) 1/1
(B) 10/1
(C) 1/10
(D) 1/100
(E) None of the Above
Rationale: 1.0% =1/1
Answer is A.
Answer: (A) 1/1
Question: If four coins are tossed, the probability of getting two heads and two tails is ?
(A) 3/8
(B) 3/6
(C) 3/1
(D) 3/2
(E) 3/4
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A
Answer: (A) 3/8
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 12
(B) 75
(C) 88
(D) 54
(E) 15
Rationale: S = (90 + 60)/2
= 75 kmph
Answer: B
Answer: (B) 75
Question: A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1993. She ended on her
(A) a) thumb
(B) b) the index finger
(C) c) the middle finger
(D) d) the ring finger
(E) e) the little finger
Rationale: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1993 has to be thumb
Answer is (A)
Answer: (A) a) thumb
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
(A) 88%
(B) 90%
(C) 80%
(D) 87%
(E) 20%
Rationale: A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer:C
Answer: (C) 80%
Question: Twice as many students attend math class compared to people who attend history class. If 2 people began attending history class instead of math class, the ratio of math students to history students would be 1 to 1. How many students total attend these two classes? Hint: No students attend both math and history class.
(A) 12
(B) 16
(C) 90
(D) 36
(E) None of the Above
Rationale: By checking the answer choices:
Since we have an initial ratio of 2:1, the total count should be divisible by 3.
A. 12/3=4, Math Students = 8, History Students = 4, Since 8-2 is equal to 4+2 this is the correct answer.
B. Out, Since not divisible by 3.
C. 90/3=30, Math Students = 60, History Students = 30, Since 60-2 is not equal to 30+2, this is not the answer.
D. 36/3=12, Math Students = 24, History Students = 12, Since 24-2 is not equal to 12+2 this as well can not be the answer.
E. Since choice A is correct, choice E is not correct.
A is the correct answer.
Answer: (A) 12
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 99.
(A) 1378
(B) 2988
(C) 2777
(D) 26877
(E) 2500
Rationale: No explanation is available for this question!
ANSWER: E
Answer: (E) 2500
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 2881
(C) 2887
(D) 9977
(E) 2212
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630.Answer: A
Answer: (A) 3630
Question: The cost price of a radio is Rs.4500 and it was sold for Rs.3200, find the loss %?
(A) 28.9%
(B) 22%
(C) 28%
(D) 45%
(E) 32%
Rationale: 4500 ---- 1300
100 ---- ? => 28.9%
Answer:A
Answer: (A) 28.9%
Question: A committee of three people is to be chosen from 8 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 469
(B) 468
(C) 428
(D) 248
(E) 448
Rationale: Total no of ways of choosing a committee =16C3 = 560
No of ways to choose first couple = 8C1 = 8
No of ways to choose 1 person from remaining 14 = 14C1 = 14
Total number of ways of choosing a married couple to be in the same committee = 8*14=112
So, no of ways not choosing a married couple = 560-112=448
ANS:E. 448
Answer: (E) 448
Question: Of the teams competing in the world archery championships, Thirty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
(A) 10/20
(B) 30/20
(C) 13/15
(D) 17/20
(E) 13/17
Rationale: Half as manymeans half of EU, then
EU 30%
US 15%
AF 5%
the rest is 50%, answer A
Answer: (A) 10/20
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. 64 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.8 years and the standard deviation is 2.4 years, what percent of the distribution has more than 10.2 years as a shelf’s average life?
(A) 15%
(B) 16%
(C) 17%
(D) 18%
(E) 19%
Rationale: Average = 7.8
SD = 2.4
7.8 - 2.4 < 64% of distribution < 7.8 + 2.4
5.4 < 64% of distribution < 10.2
36% is outside this range.
Given: Distribution is symmetric. So 18% of distribution is less than 5.4 and the other 18% of distribution is greater than 10.2.
Answer: D
Answer: (D) 18%
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) 322
(B) 480
(C) 287
(D) 192
(E) 107
Rationale: Explanation:
SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer: B
Answer: (B) 480
Question: What is the sum of all possible solutions to |x - 4|^2 + |x - 4| = 12 ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Denote |x - 4| as y: y^2 + y = 12 --> y = -4 or y = 3. Discard the first solution since y = |x - 4|, so it's an absolute value and thus cannot be negative.
y = |x - 4| = 3 --> x = 7 or x = 0. The sum = 7.
Answer: E.
Answer: (E) 7
Question: The sum of the even numbers between 1 and k is 79*80, where k is an odd number, then k=
(A) 79
(B) 80
(C) 81
(D) 157
(E) 159
Rationale: The number of terms in this set would be: n=(k-1)/2 (as k is odd)
Last term: k-1
Average would be first term+last term/2=(2+k-1)/2=(k+1)/2
Also average: sum/number of terms=79*80/((k-1)/2)=158*80/(k-1)
(k+1)/2=158*80/(k-1) --> (k-1)(k+1)=158*160 --> k=159
Answer E.
Answer: (E) 159
Question: A train 500 m long can cross an electric pole in 50 sec and then find the speed of the train?
(A) 76 Kmph
(B) 54 Kmph
(C) 72 Kmph
(D) 34 Kmph
(E) 36 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 500/50
S = 10 M/Sec
Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 36Kmph
Answer: E
Answer: (E) 36 Kmph
Question: If a committee of 2 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
(A) 20
(B) 40
(C) 50
(D) 80
(E) 120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) each to send onerepresentativeto the committee: 5C2=10.
But these 2 chosen couples can send two persons (either husband or wife): 2*2=2^2=4.
Total # of ways: 5C2*2^2=40.
Answer: B.
Answer: (B) 40
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
(A) 1365
(B) 1452
(C) 1204
(D) 4578
(E) 1852
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15C4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: A
Answer: (A) 1365
Question: Two persons start at the same point, walk in opposite directions with 6 km/hr and 6 km/hr respectively.
What is the distance separated after 3 and half hrs?
(A) 26.250 km
(B) 42 km
(C) 44 km
(D) 48 km
(E) 25.250 km
Rationale: As the two persons are moving in the opposite direction, so they will be separateed in 1 hour = 6 + 6 = 12 km.
They will be separated in 3.5 hours = 12 * 3.5 = 42 km
ANSWER:B
Answer: (B) 42 km
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1
Question: The length of rectangle is thrice its breadth and its perimeter is 72 m, find the area of the rectangle?
(A) 432
(B) 212
(C) 243
(D) 992
(E) 212
Rationale: 2(3x + x) = 72
l = 27 b = 9
lb = 27 * 9 = 243
Answer:C
Answer: (C) 243
Question: The ratio between the sale price and the cost price of an article is 4:3. What is the ratio between the profit and the cost price of that article?
(A) 2:9
(B) 2:5
(C) 3:6
(D) 2:0
(E) 1:3
Rationale: Let C.P. = Rs. 3x and S.P. = Rs. 4x.
Then, Gain = Rs. x
Required ratio = x : 3x = 1:3
Answer:E
Answer: (E) 1:3
Question: When a random experiment is conducted, the probability that event A occurs is 1/3. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice?
(A) 5/243
(B) 25/243
(C) 64/243
(D) 80/243
(E) 16/17
Rationale: one case is:
1/3*1/3*2/3*2/3*2/3=2^3/3^5
we have 5!/2!*3!=10 such cases
so, 2^3*10/3^5=80/243
Answer: D.
Answer: (D) 80/243
Question: A man took loan from a bank at the rate of 12% p.a. S.I. After 20 years he had to pay Rs. 1500 interest only for the period. The principal amount borrowed by him was?
(A) 625
(B) 700
(C) 950
(D) 825
(E) 630
Rationale: Principal = (100 * 1500) / (12 * 20)
= Rs.625
Answer: A
Answer: (A) 625
Question: The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability Z that Tommy CANNOT form a triangle from the 3 sticks?
(A) 11/32
(B) 13/32
(C) 15/32
(D) 17/32
(E) 19/32
Rationale: In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!
1,3,4 (4=1+3): 6 ways of arriving at this
2,2,4 (4=2+2): 3 ways of arriving at this
1,1,3 (3>1+1): 3 ways of arriving at this
1,2,3 (3=1+2): 6 ways of arriving at this
1,1,2 (2+1+1): 3 ways of arriving at this
Overall favourable outcomes: 30
Total outcomes: 4*4*4 = 64 (4 ways of choosing a stick from each of the 3 bags)
Probability Z that a triangle is not formed = 30/64 = 15/32
C is the correct option here.
Answer: (C) 15/32
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?
(A) 10
(B) 11
(C) 22
(D) 15
(E) 18
Rationale: i) Let the ages of the five members at present be a, b, c, d & e years.
And the age of the new member be f years.
ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)
iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years
So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)
==> a + b + c + d + e = 5x + 15
==> a + b + c + d = 5x + 15 - e ------ (3)
iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,
The new average is: (5x + 15 - e + f)/5
Equating this to the average age of x years, 3 yrs, ago as in (2) above,
(5x + 15 - e + f)/5 = x
==> (5x + 15 - e + f) = 5x
Solving e - f = 15 years.
Thus the difference of ages between replaced and new member = 15 years.
Answer: D
Answer: (D) 15
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required ?
(A) 88 feet
(B) 86 feet
(C) 84 feet
(D) 82 feet
(E) 83 feet
Rationale: Explanation:
We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 680
=> Breadth = 34 feet
Area to be fenced = 2B + L = 2*34 + 20
= 88 feet
Answer: Option A
Answer: (A) 88 feet
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.0 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 50 worth of diesel fuel?
(A) 20 seconds
(B) 2 minute 5 seconds
(C) 1 minute 20 seconds
(D) 20 minutes
(E) 1 hour 20 minutes
Rationale: 2 gal / 5 sec
$1.0 / gal
$50/$1.0 = 50 gal
2 gal / 5 sec with 50 gal = 125 sec
B. 2 minute 5 seconds
Answer: (B) 2 minute 5 seconds
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 8 boys when a boy gets any no. of prizes?
(A) 3096
(B) 4092
(C) 8096
(D) 4096
(E) 70
Rationale: Ans.(D)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 8 ways, i.e. (8 x 8 x 8) ways = 83 ways = 4096 ways Or nr ways = 83 ways = 4096 ways
Answer: (D) 4096
Question: A taxi company charges $1.25 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?
(A) 4 miles
(B) 4 1/4 miles
(C) 4 3/4 miles
(D) 5 1/2 miles
(E) 6 1/3 miles
Rationale: If we start out with $4.90 and have to spend $1.25 for the first quarter-mile, we will have $3.65 left to spend on quarter-mile intervals.
Since $3.65/$0.15 = 24.33 we can buy 24.33 more quarter-miles, and will travel 25.33 quarter miles in all:
25.33 × 1/4 =6 1/3 miles.
The correct answer is choice (E).
Answer: (E) 6 1/3 miles
Question: How many combinations of three letters taken from letters (a, a, b, b, c, c, d) are possible?
(A) 12
(B) 13
(C) 35
(D) 36
(E) 56
Rationale: Combinations only... total 13
So 4C3 for abcd - 4 choices
3 more for aa(b,c or d)
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 13
(Answer B)
Answer: (B) 13
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) 4551
(B) 4771
(C) 4991
(D) 4881
(E) 4661
Rationale: Let the sale in the sixth month =x
Then (6435+6927+6855+7230+6562+x)/6 =6500
=> 6435+6927+6855+7230+6562+x =6×6500
=> 34009+x=39000
=> x=39000−34009=4991
Answer is C.
Answer: (C) 4991
Question: A+B+C+D=D+E+F+G=G+H+I=17 given A=4. Find value of G and H?
(A) 2,9
(B) 3,9
(C) 1,9
(D) 4,9
(E) 5,9
Rationale: A+B+C+D=17
4+2+6+5=17
D=5
D+E+F+G=17
5+3+8+1=17
G=1
G+H+I=17
1+9+7=17
G=1,H=9.
ANSWER:C
Answer: (C) 1,9
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 766 m
(B) 156 m
(C) 215 m
(D) 156 m
(E) 156 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30 = 25/2
==> 2(160 + X) = 750 ==> X
= 215 m.
Answer: C
Answer: (C) 215 m
Question: If 3rd December 1999 is Sunday, what day is 3rd January 2000?
(A) Tuesday
(B) Thursday
(C) Sunday
(D) Friday
(E) Wednesday
Rationale: 3rd decmber is Sunday
i.e. 10th,17th,24th,31st dec also sunday
so 1st jan =mon,2nd jan=tues and 3rd jan wednesday
ANSWER:E
Answer: (E) Wednesday
Question: If a certain number is divided by 9, the quotient, dividend, and divisor, added together, will amount to 69. What is the number?
(A) 18
(B) 28
(C) 48
(D) 38
(E) 54
Rationale: Let x = the number sought.
Then x/9 + x + 9 = 69.
And x = 54.
E
Answer: (E) 54
Question: The total weight of six nougat nuggets is 2 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
(A) 0.33 oz.
(B) 0.5 oz.
(C) 1.8 oz.
(D) 5 oz.
(E) 18 oz
Rationale: Average = Total/Number of items
= 2/6 = 0.33.
Hence, A
Answer: (A) 0.33 oz.
Question: The total of the ages of Amar, Akbar and Anthony is 45 years. What was the total of their ages three years ago ?
(A) 36
(B) 44
(C) 66
(D) 16
(E) 18
Rationale: Explanation:
Required sum = (45 - 3 x 3) years = (45 - 9) years = 36 years.
Answer: A
Answer: (A) 36
Question: Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 45%. What fraction of the original paint was replaced?
(A) 1/30
(B) 1/5
(C) 2/3
(D) 3/4
(E) 4/5
Rationale: 45% is 20%-points above 25% and 5%-points below 50%.
Thus the ratio of 25%-solution to 50%-solution is 1:4.
1/5 of the original paint was replaced.
The answer is B.
Answer: (B) 1/5
Question: 8 persons can build a wall 140m long in 42 days. In how many days can 30 persons complete a similar wall 100 m long?
(A) 12
(B) 10
(C) 8
(D) 6
(E) 5
Rationale: Explanation :
More persons, less days(indirect proportion)
More length of the wall, more days(direct proportion)
⇒ 8 × 100 × 42 = 30 × 140 × x
⇒ x = (8 × 100 × 42)/(30 × 140) = (8 × 100 × 14)/(10 × 140) = (8 × 100)/(10 × 10) = 8. Answer : Option C
Answer: (C) 8
Question: If 35% of a number is 12 less than 50% of that number, then the number is?
(A) 40
(B) 50
(C) 60
(D) 80
(E) 70
Rationale: Let the number be x. Then,
50% of x - 35% of x = 12
50/100 x - 35/100 x = 12
x = (12 * 100)/15 = 80.
ANSWER:D
Answer: (D) 80
Question: The expression (5x-2)/(x-3) is equivalent to which of the following?
(A) (5-2)/3
(B) 5 – (2/3)
(C) 5 – (x)/(x+3)
(D) 5 – (17)/(x+3)
(E) 5 + (13)/(x+3)
Rationale: Easiest way is to pick any number and put in (5x-2)/(x-3). Then check the options with the same number.
I took x=1 and got E as the answer.
Answer: (E) 5 + (13)/(x+3)
Question: 8 persons a, b, c, ... and h are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?
(A) 24
(B) 36
(C) 480
(D) 1720
(E) 4320
Rationale: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..
total 8 are there..
take a,b, and c as one,so total =6..
these 6 can be arranged in 6! ways..
a,b, and c can be arranged within themselves in 3! ways ..
TOTAL = 6!*3!=4320
E
Answer: (E) 4320
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
(A) 2
(B) 4
(C) 6
(D) 5
(E) 7
Rationale: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
Answer: (D) 5
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
(A) 4.04%
(B) 4.00%
(C) 4.14%
(D) 5.04%
(E) None
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
A
Answer: (A) 4.04%
Question: If 8 workers can build 8 cars in 8 days, then how many days would it take 7 workers to build 7 cars?
(A) 4
(B) 7
(C) 8
(D) 12
(E) 14
Rationale: 8 workers can build 1 car per day on average.
1 worker can build 1/8 of a car per day.
7 workers can build 7/8 car per day.
The time required to build 7 cars is 7 / (7/8) = 8 days
The answer is C.
Answer: (C) 8
Question: 0, 1, 3, 6, 7, 9, 12, 13, 15, 18, ?.
What number should replace the question mark?
(A) 13
(B) 19
(C) 12
(D) 44
(E) 75
Rationale: B
19
The sequence progresses +1, +2, +3 repeated;
Answer: (B) 19
Question: If the speed of a man is 54 km per hour, then what is the distance traveled by him in 25 seconds ?
(A) 275m
(B) 360m
(C) 375m
(D) 420 m
(E) 440 m
Rationale: The distance traveled in 25 sec = 54*(5/18) *25 =375m
ANSWER:C
Answer: (C) 375m
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.
(A) 298 km
(B) 278 km
(C) 278 km
(D) 300 km
(E) 267 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300
= 11 => x
= 300 km
Answer:D
Answer: (D) 300 km
Question: 2^(15) + 2^(16) + 2^(17) + ... + 2^(44) + 2^(45) =
(A) 2^15(2^(29)-1)
(B) 2^15(2^(31)-1)
(C) 2^16(2^(25)-1)
(D) 2^12(2^(20)-1)
(E) 2^14(2^(30)-1)
Rationale: 2^(15) + 2^(16) + 2^(17) + ... + 2^(44) + 2^(45) =
2^(15)*(1+2+4+...+2^(30)) =
2^(15)*(2^(31) - 1)
The answer is B.
Answer: (B) 2^15(2^(31)-1)
Question: What is the lowest possible common multiple Y of 2 distinct integers, each greater than 329?
(A) 330·331
(B) 330^2
(C) 33·331
(D) 660
(E) 330
Rationale: Lowest possible common multiple Y of 2 distinct integers will have to be multiple of the number greater than 329...which 330..
so one number will be 330...another one will be 660..
Ans is D.
Answer: (D) 660
Question: In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket inchours, and the hot-water leak alone would fill the same bucket inhhours, wherec < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it tookthours to fill the bucket, which of the following must be true?
I. 0 < t < h
II. c/2 < t < h/2
III. c < t < h
(A) a) I only
(B) b) II only
(C) c) III only
(D) d) I and II
(E) e) I and III
Rationale: I picked numbers for this problem
C = 2 hours
H = 3 hours
C<H
2 people working together formula is
1/C + 1/H = 1/t
1/2 + 1/3 = 1/t
t = 6/5 = 1.2
Substitute the values of C, H and t in the 3 choices given below
Only 1, 2 are valid.Therefore D is the best answer
Answer: (D) d) I and II
Question: The cash difference between the selling prices of an book at a profit of 2% and 4% is $3. The ratio of the two selling prices is:
(A) 55:23
(B) 52:33
(C) 51:52
(D) 45:53
(E) 51:34
Rationale: Let C.P. of the book be $x.
Then, required ratio = 102% of x / 104% of x
= 102/104 = 51/52 = 51:52
C
Answer: (C) 51:52
Question: The average of 13 numbers is 15.8. If the average of the first seven numbers is 15.6 and that of the last seven numbers is 15.4,then the middle number is?
(A) 12.6
(B) 11.6
(C) 12.8
(D) 12.9
(E) 12.5
Rationale: Middle number = 15.6*7 + 15.4*7- 15.8*13 = 109.2+107.8-205.4=11.6
Answer is B
Answer: (B) 11.6
Question: A person can row at 9 kmph and still water. He takes 8 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 32
(B) 38
(C) 29
(D) 54
(E) 20
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 8.5
=> x/10 + x/8 = 17/2 => (4x + 5x)/40 = 17/2 => x
= 38 km.
Answer:B
Answer: (B) 38
Question: I brought 30 books on Mathematics, Physics, and Chemistry, priced at Rs.17, Rs.19, and Rs.23 per book respectively, for distribution among poor students of Standard X of a school. The physics books were more in number than the Mathematics books but less than the Chemistry books, the difference being more than one. The total cost amounted to Rs.620. How many books on Mathematics, Physics, and Chemistry could have been bought respectively?
(A) 5, 8, 17
(B) 5, 12, 13
(C) 5, 10, 15
(D) 5, 6, 19
(E) None of these
Rationale: Explanation :
Given, Total amount=620 ( last digit is 0 ).
So find the last digit of product number of books and price of one book.
option 1, 7*5 + 9*8 + 3*7 = 5+2+1 = last digit 8 is not 0.
option 2, 7*5 + 9*2 + 3*3 = 5+8+9 = last digit is not 0.
option3, 5*7 + 10*9 + 5*5 = 5+0+5= last digit is 0.
option4, 5*7 + 6*9 + 3*9 = 5+4+7=6 last digit is not 0.
Hence, only 3rd option satisfy this condition.
Answer : C
Answer: (C) 5, 10, 15
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
(A) 9%loss
(B) 3%loss
(C) 5%loss
(D) 7%loss
(E) 2%loss
Rationale: (30*30)/100
= 9%loss
Answer: A
Answer: (A) 9%loss