mathewhe/aqua_rat huggingface dataset:
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 1% p.a. in 9 years. What is the sum?
(A) 42315
(B) 42877
(C) 44625
(D) 38925
(E) 22887
Rationale: Principal = (100 * 4016.25) / (1 * 9)
= Rs.44625.
Answer:C
Answer: (C) 44625
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 14-meter platform and caught it after it had traveled 41.7 meters. How many times did the ball bounce?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Ans: 6
Division of total diatance travelled will be 14+14+7+3.5+1.75+0.9+0.5 ANS B
Answer: (B) 6
Question: When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 2
Rationale: Let n=6 (leaves a remainder of 6 when divided by 24)
3n = 3(6) =18, which leaves a remainder of 2 when divided by 8.
Answer E
Answer: (E) 2
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
(A) 197
(B) 240
(C) 279
(D) 268
(E) 269
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer:B
Answer: (B) 240
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
(A) 42 6/8%
(B) 42 4/7%
(C) 43 6/7%
(D) 42 6/7%
(E) 42 6/9%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: (D) 42 6/7%
Question: How many distinct integer values of n satisfy the inequality||n-3| + 4| ≤ 14?
(A) 15
(B) 12
(C) 17
(D) 18
(E) 19
Rationale: so i can write this as In-3I+4<=14
or In-3I<=10
so n can have -7 to 13 = 12 true values....
B
Answer: (B) 12
Question: Edward walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:10. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 16 meters. What is Edward's speed in meters per minute?
(A) 108
(B) 160
(C) 198
(D) 216
(E) 252
Rationale: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×16(per block dist)
Speed = 1600mts/10min =160m/min
B is the answer
Answer: (B) 160
Question: Of the 600 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 30 percent ?
(A) 200
(B) 160
(C) 112
(D) 257
(E) 56
Rationale: Original (Long-Term is 70%)
Total = 600
Long-Term = .7(600) =420
New (Long-Term is 30%)
New Total = 800 - y
New Long-Term = 420 - y
420 - y = .3 (800 - y)
y = 257
Answer: D
Answer: (D) 257
Question: Find the largest 4 digit number which isexactly divisible by 88?
(A) 5678
(B) 7654
(C) 9944
(D) 9950
(E) 10000
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: (C) 9944
Question: If m is an integer such that (-2)^2m=2^(12-m) then m=?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: (-2)^(2m) = 4^m
and
2^(12-m) = 4^((12-m)/2)
Therefore,
m = (12-m)/2
2m = 12 - m
m = 4
Answer C
Answer: (C) 4
Question: The value of 99^(92/99) x 99 is:
(A) 9989
(B) 9893
(C) 9890
(D) 9809
(E) 9810
Rationale: (100 â€“ 7/99) x 99 = 9900 â€“ 7
= 9893.
ANSWER:B
Answer: (B) 9893
Question: 3660÷12÷5=?
(A) 61
(B) 67
(C) 89
(D) 54
(E) 32
Rationale: 3660 ÷ 12 = 305
305 ÷ 5 = 61
Answer is A
Answer: (A) 61
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?
(A) 10
(B) 20
(C) 30
(D) 35
(E) 43
Rationale: His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.25-1)* 100 = 20
B
Answer: (B) 20
Question: Jackson invested $700,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
(A) $115,384
(B) $120,000
(C) $121,072
(D) $124,129
(E) $130,000
Rationale: x be the amount invested in account P
0.12*x +(300000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$130,000
hence answer is E
Answer: (E) $130,000
Question: 14 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
(A) 144
(B) 131
(C) 115
(D) 189
(E) 45
Rationale: there are 14 business exec and in each handshake 2 business execs are involved.
hence 14C2=91
Also, each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake.
total=91+98=189
ANS: D
Answer: (D) 189
Question: Sunil invested $ 2200 fir 2 years and $ 2100 for 3 years at the same rate of Simple Interest. If the total interest from these investments is $ 1400, what is the rate of interest?
(A) 12 3/4%
(B) 12 %
(C) 13 %
(D) 16%
(E) 13 2/4%
Rationale: (2200x2xR)/100+(2100x3xR)/100=1400
107R=1400
R= 13 %
Answer is C
Answer: (C) 13 %
Question: If two dice are thrown together, the probability of getting an even number on both dice is
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/3
(E) 1/2
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on both dies is 9/36 = 1/4
P(E) = 1/4.
A)
Answer: (A) 1/4
Question: At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 30 males did not bring gifts to the party, how many females did bring gifts?
(A) 18
(B) 28
(C) 40
(D) 68
(E) 70
Rationale: the correct method
total = 300..
70% of 300 = 210 got gifts..
90 did not get gift, out of which 30 are males, so remaining 90-30=60 are females..
But 40% females brought gift, so 60% did not get it..
so 60% = 60, 100%= 60*100/60= 100.
ans 40% of 100 =40
C
Answer: (C) 40
Question: In a exam there are 26 number of question. For one write question add 8 marks and for one wrong 5 marks subtract. One candidate answered all questions. His marks is 0. How many answers was correct?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: let no. of right ques be x,
then no. of wrong ques will be= 26 - x
now, according to ques
8x - (26-x)5 = 0,
hence x=10...no. of right ques is 10
ANSWER:B
Answer: (B) 10
Question: Five bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 seconds respectively. In 20 minutes, how many times do they toll together?
(A) 11
(B) 10
(C) 15
(D) 16
(E) 17
Rationale: L.C.M of 2,4,6,8,10 is 240. i.e after each 2 min they will toll together.So in 20 min they will toll 10 times.As they have initially tolled once,The answer will be 10+1=11.
ANSWER:A
Answer: (A) 11
Question: X, Y and Z are inner angles in a triangle. If X= Y+ Z, what can't be the size of Y?
(A) 30 DEGREES
(B) 90 DEGREES
(C) 60 DEGREES
(D) 70 DEGREES
(E) 950 DEGREES
Rationale: Given X= Y+ Z, and X, Y and Z are inner angles in a triangle. Thus X+ Y+ Z= 180
Y+ Z+ Y+ Z= 180 => 2(Y+ Z) = 180 => Y+ Z= 90. Thus Y will be less than 90.
Hence the answer is B.
Answer: (B) 90 DEGREES
Question: Fathers age is 5 times his son’s age. 4 years back the father was 9 times older than son.Find the fathers’ present age.
(A) 40 years
(B) 33 years
(C) 22 years
(D) 33 years
(E) 44 years
Rationale: Ans. 40 years
Answer: (A) 40 years
Question: A little boy is flying a kite. The string of the kite makes an angle of 30o with the ground. If the height of the kite is h = 24 m, find the length (in meters) of the string that the boy has used.
(A) 56
(B) 28
(C) 48
(D) 24
(E) 26
Rationale: Answer: C
Answer: (C) 48
Question: Think of a number, divide it by 5 and add 23 to it. The result is 42. What is the number thought of?
(A) 24
(B) 77
(C) 297
(D) 267
(E) 95
Rationale: Explanation :
42-23 = 19
19 x 5 = 95
Answer : E
Answer: (E) 95
Question: The angles of a triangle are in the ratio 3: 6 : 1. Find the measurement of the 3 angles of triangle.
(A) 108°
(B) 24°
(C) 58°
(D) 18°
(E) 54°
Rationale: If the ratio of the three angles is 3:6:1, then the measures of these angles can be written as 3x, 6x and x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
3x + 6x + x = 180
Solve for x
10x = 180
x =18
The measures of the three angles are
3x =3 x18=54°
6x = 6 × 18= 108°
x = 1 × 18 = 18°
D
Answer: (D) 18°
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) Rs.18,828.80
(B) Rs.19,828.80
(C) Rs.18,028.80
(D) Rs.17,828.80
(E) None of these
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
ANSWER:B
Answer: (B) Rs.19,828.80
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions?
(A) 708 m
(B) 704 m
(C) 774 m
(D) 714 m
(E) 563.2 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 400 * 2 * 22/7 * 22.4 = 56320 cm
= 563.2 m
Answer:E
Answer: (E) 563.2 m
Question: A wheel of a car of radius 21 cms is rotating at 700 RPM. What is the speed of the car in km/hr?
(A) 79.2 km/hr
(B) 55.44 km/hr
(C) 7.92 km/hr
(D) 39.6 km/hr
(E) 3.96 km/hr
Rationale: Explanatory Answer
The radius of the wheel measures 21 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.
In a minute, the distance covered by the wheel = circumference of the wheel * rpm
∴ this wheel will cover a distance of 132 * 700 = 92400 cm in a minute.
In an hour, the wheel will cover a distance of 92400 * 60 = 5544000 cm.
Therefore, the speed of the car = 5544000 cm/hr = 55.44 km/hr
Choice B is the correct answer.
Answer: (B) 55.44 km/hr
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) 90%
(B) 88%
(C) 80%
(D) 90%
(E) 84%
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: What will be the compound interest on a sum of Rs. 20,000 after 3 years at the rate of 12% p.a.?
(A) Rs. 8098.56
(B) Rs. 9720
(C) Rs. 10123.20
(D) Rs. 10483.20
(E) None
Rationale: Amount = [20000 * (1 + 12/100)^3]
= 20000 * 28/25 * 28/25 * 28/25 = Rs. 28098.56
C.I. = (28098.56 - 20000) = Rs. 8098.56
ANSWER:A
Answer: (A) Rs. 8098.56
Question: How many minutes does it take John to type y words if he types at the rate of v words per minute?
(A) x/y
(B) y/v
(C) xy
(D) 60x/y
(E) y/(60x)
Rationale: time*rate=job --> time*v=y --> time=y/v.
Answer: B.
Answer: (B) y/v
Question: What is the next number of the following sequence
1,3,4,5,6,7,8,1,9,16,25,36,49...
(A) 64
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: (1, 3 ,4, 5, 6, 7, 8) (1, 9, 16, 25, 36, 49, x)
square of 1st group gives 2nd group
1^2 = 1
3^2 = 9
4^2 = 16
5^2 =25
6^2 =36
7^2 = 49
8^2=64
ANSWER:A
Answer: (A) 64
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?
(A) 181
(B) 197
(C) 120
(D) 123
(E) 179
Rationale: Let speed of the car be x km/hr.
Then, speed of the train = 150/100 x = 3/2 x km/hr.
75/x - 75/(3/2 x) = 125/(10 * 60)
75/x - 50/x = 5/24 = 120 km/hr.
Answer:C
Answer: (C) 120
Question: In the xy-coordinate plane, the graph of y = -x^2 + 4 intersects line L at (p,5) and (t,-7). What is the least possible value of the slope of line L?
(A) 6
(B) 2
(C) -4
(D) -6
(E) -10
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving
5 = -p2 +4
p2 = 1
p = + or - 1
simillarly point (t,-7) should satisfy the equation. hence x=t and Y=-7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (-7-5)/(4-1) = -4
IMO option C is correct answer.
Answer: (C) -4
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
(A) 9268
(B) 9261
(C) 9262
(D) 9242
(E) 9266
Rationale: A = 8000(21/20)3 = 9261
Answer: B
Answer: (B) 9261
Question: Two friends want to buy a snack. They combine their money and find they have $3.80, consisting of quarters, dimes, and nickels. If they have 34 coins and the number of quarters is half the number of nickels, how many quarters do they have?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let x be the number of quarters. Then 2x is the number of nickels.
(1) 25x + 10x + 10D = 380. Then 7x + 2D = 76
(2) 3x + D = 34. Then 6x + 2D = 68
Let's subtract equation (2) from equation (1).
x = 8
The answer is B.
Answer: (B) 8
Question: Rajani has to read a book of 445 pages. She has already read the first 157 pages of the book and if she reads 24 pages of the book everyday then how long will she take now to complete the book?
(A) 25 days
(B) 20 days
(C) 46 days
(D) 21 days
(E) None of these
Rationale: Remaining pages to read = 445 – 157 = 288
∴ Reqd. number of days = 288⁄24 = 12
Answer E
Answer: (E) None of these
Question: Twenty percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the men are science majors if 40% of the class are men?
(A) 2%
(B) 5%
(C) 20%
(D) 30%
(E) 45%
Rationale: Science majors make up 0.2 of the class.
60% of the class are women and 0.2*0.6 = 0.12 of the class are female science majors.
Then 0.08 of the class are male science majors.
0.4x = 0.08
x = 0.2 = 20%
The answer is C.
Answer: (C) 20%
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 630, what is the least possible value of n?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 630 = 2*3*3*5*7, so n must be at least 7.
The answer is C.
Answer: (C) 7
Question: Six female friendssix male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?
(A) 1036800
(B) 1680
(C) 1152
(D) 576
(E) 70
Rationale: now any of the alternate 6 places can be filled by 6 male or female in 6!
similarily,
other 6 alternate places can be filled in 6!
hence required probability= 2*6!*6!= 10,36,800
hence A
Answer: (A) 1036800
Question: In the land of the famous milkman Merghese Durian, a milkman sells his buffalo for Rs. 720 at some profit. Had he sold his buffalo at Rs. 510, the quantum of the loss incurred would have been double that of the profit earned. What is the cost price ?
(A) 650
(B) 750
(C) 450
(D) 550
(E) 600
Rationale: Let CP be c
c-510=2(720-c)
c=650
ANSWER:A
Answer: (A) 650
Question: The average of 7 numbers is 26. If each number be multiplied by 5. Find the average of new set of numbers?
(A) A)110
(B) B)122
(C) C)120
(D) D)125
(E) E)130
Rationale: Explanation:
Average of new numbers = 26 * 5 = 130
Answer: Option E
Answer: (E) E)130
Question: On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.40 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027
(B) 0.09
(C) 0.417
(D) 0.784
(E) 0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.4
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.6 * 0.4 = 0.24
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program = 0.6^2 * 0.4 = 0.144
Total = 0.784
Ans D
Answer: (D) 0.784
Question: The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:
(A) Rs. 1325
(B) Rs. 1300
(C) Rs. 1350
(D) Rs. 1500
(E) Rs. 1600
Rationale: time=1/2yr
r=8%
let pw=x
si=1404-x
x*1/2*8/100=1404-x.(ref problm 10 of SI ,rs aggarwal)
x=1404*25/26
hence x=1350
ANSWER:C
Answer: (C) Rs. 1350
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 80 percent of b, what is the value of m/x?
(A) 1/7
(B) 3/4
(C) 4/5
(D) 5/4
(E) 3/2
Rationale: a/b = 4/5
m/x = (1/5)*5 / (7/4)*4 = 1/7
The answer is A.
Answer: (A) 1/7
Question: The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?
(A) 18
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Type 1 cost = 15
type 2 cost = 20
=>2:3
hence cost the mixture= (15*2)+(20*3) /(2+3) = 18
ANSWER A
Answer: (A) 18
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 37
(B) 38
(C) 22
(D) 90
(E) 28
Rationale: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 480 16x = 480 x = 30.
Hence, total number of notes = 3x = 90.
Answer:D
Answer: (D) 90
Question: If 0 < a < b and k = (6a + 7b)/b , which of the following must be true?
(A) k < 2
(B) k < 7
(C) k < 9
(D) k > 15
(E) k < 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a < b, you get k = (6+14)/2 = 10. This eliminates all but option E, making it the correct answer.
Answer: (E) k < 11
Question: If M:N is 2:9 and N:P is 9:4 then M:P is equal to
(A) 1:4
(B) 1:3
(C) 5:2
(D) 3:2
(E) 1:2
Rationale: The two ratios given are having the same number 9 for N in both the ratios.
Hence- M:N = 2:9 N:P = 9:4
=> M:P = 2:4 = > 1:2
Answer E
Answer: (E) 1:2
Question: 1,2,3,2,4,6,4,8,_____
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Divide the series:
1,2,3
2,4,6
4,8,?
so it is 12
ANSWER:C
Answer: (C) 12
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 2:9
(B) 6:7
(C) 6:5
(D) 2:9
(E) 3:5
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer: C
Answer: (C) 6:5
Question: Jack and Christina are standing 240 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 5 feet per second and Christina walks in a straight line toward Jack at a constant speed of 3 feet per second. Lindy runs at a constant speed of 9 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
(A) 180
(B) 210
(C) 240
(D) 270
(E) 300
Rationale: The relative speed of Jack and Christina is 5 + 3 = 8 feet per second.
The distance between them is 240 feet, hence they will meet in (time) = (distance)/(relative speed) = 240/8 = 30 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 9*30 = 270 feet.
Answer: D.
Answer: (D) 270
Question: In a group of cows and hens, the number of legs are 8 more than twice the number of heads. The number of cows is :
(A) 5
(B) 6
(C) 7
(D) 10
(E) 4
Rationale: Let no of cows be x, no of hens be y.
So heads=x+y
Legs=4x+2y
Now, 4x+2y = 2(x+y)+ 8
2x = 8
x = 4.
ANSWER:E
Answer: (E) 4
Question: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/4, then the reciprocal of n must be
(A) Less than -2
(B) Between -1 and -1/2
(C) Between -1/2 and 0
(D) Between 0 and 1/2
(E) Greater than 2
Rationale: n^2 < 1/4
abs(n) < 1/2
Since n<0, then 0 > n > -1/2
1/n < -2
The answer is A.
Answer: (A) Less than -2
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 100
(B) 150
(C) 200
(D) 240
(E) 230
Rationale: The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
C
Answer: (C) 200
Question: how many 3 digit numbers can be formed with 2 consecutive same numbers .
(A) 160
(B) 171
(C) 180
(D) 256
(E) 352
Rationale: if you fix the 2nd and 3rd position which can be done in 10 ways and 1st position can take value from 1-9 therefore total ways comes out to b 9*10=90
plus
if you fix the 1st nd 2 position which can be done in 9 ways and 3rd position can take 10 values i.e from 0-9, that makes it 9*10=90
total=90+90=180
now minus the common part like 111,222 to 999
that is total of 9 numbers..
therefore finally 180-9=171
ANSWER:B
Answer: (B) 171
Question: The C.I. on a certain sum for 2 years at 10% per annum is Rs. 525. The S.I. on the same sum for double the time at half the rate percent per annum is?
(A) Rs. 400
(B) Rs. 500
(C) Rs. 600
(D) Rs. 800
(E) Rs. 850
Rationale: Explanation:
Let the sum be Rs. P. Then,
[P(1 + 10/100)2 - p] = 525
P[(11/10)2 - 1] = 525
P = (525 * 100) / 21 = 2500
Sum = Rs. 2500
So, S.I. = (2500 * 5 * 4)/100 = Rs. 500
ANSWER IS B
Answer: (B) Rs. 500
Question: Sachin is younger than Rahul by 9 years. If the ratio of their ages is 7:9, find the age of Sachin
(A) 31.5
(B) 24.5
(C) 24.3
(D) 24.9
(E) 24.1
Rationale: If Rahul age is x, then Sachin age is x-9,
so (x-9)/x = 7/9
=> 9x-81 = 7x
=> 2x = 81
=> x = 40.5
So Sachin age is 40.5 - 9 = 31.5
Answer: A
Answer: (A) 31.5
Question: A sum of 12,500 amounts to 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 2%
(B) 1%
(C) 6%
(D) 5%
(E) 8%
Rationale: C
6%
S.I. = (15500 - 12500) = 3000.
Rate = (100 x 3000)/(12500x4)% = 6%
Answer: (C) 6%
Question: n^(n/2)=8 is true when n=8 in the same way what is the value of n if n^(n/2) =20?
(A) 8
(B) 14
(C) 10
(D) 20
(E) 40
Rationale: n^(n/2)=20Apply logN/2logn=log20nlogn=2log20=log20^2=log400Logn=log400Now apply antilogn=400/nNow n=20.ANSWER:D
Answer: (D) 20
Question: Sita has $100 in her piggy bank. How much will she have in her bank 20 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?
(A) 300
(B) 310
(C) 320
(D) 330
(E) 340
Rationale: The dollar deposits are in an A.P.
1,2,3,4...20 with common difference 1
Sum of the terms is n(n+1) / 2
i.e 20 * (20+1) /2
= 20 * 21/2 = 210
Total deposit therefore with Chiu-Lihas is 100 + 210= 310$
Answer: (B) 310
Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 255
(B) 267
(C) 225
(D) 277
(E) 211
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m. Answer:C
Answer: (C) 225