mathewhe/aqua_rat huggingface dataset:
Question: A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
(A) 400
(B) 798
(C) 452
(D) 635
(E) 432
Rationale: 2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer:A
Answer: (A) 400
Question: Henry answered 1/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?
(A) x
(B) (85/48)*x
(C) (85/36)*x
(D) (17/5)*x
(E) (85/18)*x
Rationale: Let Q be the number of homework questions.
Q = Q/5 + (5/17)(4Q/5) + x
Q = 17Q/85 + 20Q/85 + x
48Q/85 = x
Q = (85/48)*x
The answer is B.
Answer: (B) (85/48)*x
Question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
(A) 356
(B) 278
(C) 127
(D) 100
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 6 = 100 m
Answer: D
Answer: (D) 100
Question: In how many ways can 3 men & 2 women can be made from a gang of 5 men & 5 women ?
(A) 100
(B) 150
(C) 200
(D) 250
(E) 260
Rationale: Explanation:
5C3 * 5C2 = 100
A
Answer: (A) 100
Question: If the sum and difference of two numbers are 15 and 10 respectively, then the difference of their square is:
(A) 12
(B) 150
(C) 160
(D) 180
(E) 18
Rationale: Let the numbers be x and y.
Then, x + y = 15 and x - y = 10
x2 - y2 = (x + y)(x - y) = 15 * 10 = 150.
ANSWER:B
Answer: (B) 150
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 3 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A) 16
(B) 18
(C) 20
(D) 33.3
(E) 30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 50 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 3 = 9 kms/hr
Time taken = 50 / 9 = 5.55 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 5.55 = 33.3 kms... Answer - D
Answer: (D) 33.3
Question: How many miles is 150KM?
(A) 91.5miles
(B) 92.75miles
(C) 93.75miles
(D) 94.5miles
(E) 95.75miles
Rationale: 93.75miles
150/1.6
Answer:C
Answer: (C) 93.75miles
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 1:2. The first number is:
(A) A)27
(B) B)98
(C) C)34
(D) D)35
(E) E)62
Rationale: (3x-9):(5x-9) = 9:17
x = 9 => 3x = 27
Answer:A
Answer: (A) A)27
Question: Glen and Hannah drive at constant speeds toward each other on a highway. Glen drives at a constant speed of 37 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Glen is 130 km away from Hannah at 6 am, and also 130 km away from Hannah at 11 am, then how fast is Hannah driving (in kilometers per hour)?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Glen and Hannah complete 260 km / 5 hours = 52 km/hour
Hannah's speed is 52-37=15 km/hour
The answer is D.
Answer: (D) 15
Question: Four persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
(A) 625
(B) 1296
(C) 1540
(D) 1478
(E) 360
Rationale: Each person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5*5*5*5=5^4=625.
Answer: A.
Answer: (A) 625
Question: P and Q can complete a work in 10 days and 6 days respectively. P alone started the work and Q joined him after 2 days till the completion of the work. How long did the work last?
(A) 5 days
(B) 10 days
(C) 14 days
(D) 22 days
(E) 26 days
Rationale: Explanation :
Work done by P in 1 day = 1/10
Work done by Q in 1 day = 1/6
Work done by P in 2 days = 2 Ã— (1/10) = 1/5
Remaining work = 1 â€“ 1/5 = 4/5
Work done by P and Q in 1 day = 1/10 + 1/6 = 4/15
Number of days P and Q take to complete the remaining work = (4/5) / (4/15) = 3
Total days = 2 + 3 = 5
Answer : Option A
Answer: (A) 5 days
Question: A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $237 for it, the cost price of the Cricket Bat for A is:
(A) 150
(B) 120
(C) 158
(D) 160
(E) 210
Rationale: 125% of 120% of A = 237
125/100 * 120/100 * A = 237
A = 237 * 2/3 = 158.
ANSWER C
Answer: (C) 158
Question: The integers 1, 2, … , 40 are written on a blackboard. The following operation is then repeated 39
times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new
number a + b – 1 is written. What will be the number left on the board at the end?
(A) 23
(B) 122
(C) 781
(D) 377
(E) 272
Rationale: Initial sum of the number 1 to 40 = n(n+1)2=40×412=840n(n+1)2=40×412=840
After erasing two numbers a and b, and replacing with (a + b − 1), the new sum of the terms of the
sequence = 820 − 1
Similarly, after every operation, the sum of the terms of the sequence reduces by 1.
∴ The last number left (i.e. final sum) = 820 − 39 = 781
Answer:C
Answer: (C) 781
Question: Shekar scored 76, 65, 82, 62 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
(A) 74
(B) 69
(C) 75
(D) 85
(E) 90
Rationale: Explanation :
Average= (76+65+82+62+85)/5 = 370/5 =74
Hence average=74
Answer : A
Answer: (A) 74
Question: A swimmer swims downstream 55 km and upstream 10 km taking 5 hours each time; what is the speed of the current?
(A) 4.6
(B) 4.5
(C) 4.4
(D) 4.3
(E) 4.2
Rationale: 55 --- 5 DS = 11
? ---- 1
10 ---- 5 US = 2
? ---- 1 S = ?
S = (11 - 2)/2 = 4.5
Answer:B
Answer: (B) 4.5
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets.
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) 75%
Rationale: Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50 %
ANSWER IS B
Answer: (B) 50%
Question: What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 30?
(A) 884
(B) 890
(C) 892
(D) 910
(E) 945
Rationale: Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)
In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28
Number of multiples of 11*35 i.e. 385 = 1000/385 = 2
Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 884
Think: Why did I say the method is approximate in some cases?
Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)
What is the number of multiples in this case?
A
Answer: (A) 884
Question: What is the least number of cut pieces of equal length that can be cut out of two lengths 10 meters 857 millimeters and 15 meters 87 millimeters.
(A) 184
(B) 266
(C) 255
(D) 887
(E) 111
Rationale: Here, you need to find the HCF. Because, to get least number of equal cut pieces you should cut as big as possible. So, HCF of 10857 and 15087 = 141. (This is the size of each cut piece). Then the number of cut pieces = (10857 + 15087) ÷ 141 = 184.
Answer:A
Answer: (A) 184
Question: (26.3 * 12 * 20)/3+125 = ?
(A) 2339
(B) 2229
(C) 4429
(D) 5529
(E) 2669
Rationale: B
2229
? = [( 26.3 * 12 * 20)/3]+125
? = 2104 + 125 = 2229
Answer: (B) 2229
Question: How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 24
(B) 30
(C) 99
(D) 77
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 400 * 3/50 = 24 sec.
Answer: A
Answer: (A) 24
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 19.8. The difference between the unit digit and hundreds digit of that number is :
(A) a) 4
(B) b) 3
(C) c) 2
(D) d) 1
(E) e) 0
Rationale: Since the average increased by 19.8 and there were a total of 10 numbers, it means the incorrect number was 198 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 198
99c - 99a = 99(c - a) = 198
198 = 99*2 = 99(c - a)
So c - a = 2
Answer (C)
Answer: (C) c) 2
Question: Insert the missing number
5, -10, 20, -40, 80, (....)
(A) 160
(B) -160
(C) 100
(D) -100
(E) 0
Rationale: 5*-2=-10
-10*-2=20
20*-2=-40
-40*-2=80
80*-2=-160
ANSWER:B
Answer: (B) -160
Question: The average of six numbers is 27. If one number is excluded, the average becomes 25. The excluded number is
(A) 25
(B) 27
(C) 30
(D) 37
(E) 40
Rationale: Sol.
Therefore excluded number
= (27 × 6) - ( 25 × 5)
= 162 – 125
= 37.
Answer D
Answer: (D) 37
Question: In store A there are 10 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 4:3. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
(A) 3:6.
(B) 2:3.
(C) 1:3.
(D) 3:4.
(E) 3:16.
Rationale: 1st statement : ratio of pants
Store A : Store B
10x : 40x
X:4X
Price :
3y:4y
Total revenue
3xy : 16xy
3:16
Answer : E
Answer: (E) 3:16.
Question: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 165kg then find the average weight of all the 7 rounds?
(A) 94.2 kgs
(B) 88.5 kgs
(C) 86.5 kgs
(D) 67.5 kgs
(E) 88.2 kgs
Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 165/7 = 94.2 kgs
Answer:A
Answer: (A) 94.2 kgs
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 23.58
(B) 23.56
(C) 23.54
(D) 23.57
(E) 23.51
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer:D
Answer: (D) 23.57
Question: When sold at a 70% discount, a sweater nets the merchant a 40% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 78.58%
Rationale: we should be careful about what are we measuring % on/what is the base..
let the Marked up price =100..
Selling price= 100-70%of 100=30..
profit= 40%..
therefore the wholesale purchase cost= x.... 1.4x=30
or x=21.42...
marked price was 100 so ...
so answer is 78.58%..
E
Answer: (E) 78.58%
Question: How many positive factors do 120 and 80 have in common?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 24
Rationale: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 120 and 80 is 40
Number of factors of 40 = 8
Answer :A
Answer: (A) 8
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 204, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 22
(B) 36
(C) 55
(D) 77
(E) 88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 204 => .1x + 3/4x = 204 => x = 240
240 - 204 = pure gala = 36.
Answer B
Answer: (B) 36
Question: If n is an integer, then the least possible value of |35 - 6n| is?
(A) 2
(B) 3
(C) 5
(D) 0
(E) 1
Rationale: |35 - 6n| represents the distance between 35 and 6n on the number line. Now, the distance will be minimized when 6n, which is multiple of 6, is closest to 35. Multiple of 6 which is closest to 35 is 36 (for n = 6), so the least distance is 1: |35 - 36| = 1.
Answer: E.
Answer: (E) 1
Question: If MAPLE is coded as VOKZN then how will CAMEL be coded?
(A) OVNZF
(B) OUNZX
(C) OVNZX
(D) XZNVO
(E) XZNVV
Rationale: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
So each alphabet is replaced by the above rule and also whole word is reversed i.e MAPLE - after just replacing each alphabet (by above rule) we get NZKOV,then we reverse this word again and we get VOKZN.
so this way CAMEL becomes OVNZX
ANSWER:C
Answer: (C) OVNZX
Question: A, B, and C contest an election from a particular constituency. A and B together got 50% more votes than C. The vote share of A and C together is 30 percentage points more than the vote share of B. Who won the election?
(A) A
(B) B
(C) C
(D) Cannot be determined
(E) none
Rationale: Let a,b,c be the vote share of A, B, C respectively
a + b = 1.5 c
a + c = b + 30
a + b + c = 100, 2b + 30 = 100,
b = 35
a = 25, c = 40, So, C won the election.
ANSWER:C
Answer: (C) C
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
(A) 16
(B) 88
(C) 27
(D) 12
(E) 11
Rationale: Explanation:
Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
weavers &4:8 \ days& 4:8::4:x}
}4 x 4 x x = 8 x 8 x 4
x = 16.
Answer: A
Answer: (A) 16
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 18 sec
(B) 28 sec
(C) 48 sec
(D) 29 sec
(E) 24 sec
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C
Answer: (C) 48 sec
Question: (4300731)-?=2535618
(A) 1865113
(B) 1775123
(C) 1765113
(D) 1675123
(E) None of them
Rationale: Let 4300731-x=2535618
then x=4300731-2535618
=1765113
Answer is C
Answer: (C) 1765113
Question: A, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find B's share.
(A) Rs. 3240
(B) Rs. 2520
(C) Rs. 2880
(D) Rs. 3360
(E) None of these
Rationale: Explanation:
Let C's investment = Rs. x
B's investment = Rs. (x - 3000)
A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)
Now, (A + B + C)'s investment = Rs. 72000
=> x + (x - 3000) + (x + 3000) = 72000
=> 3x = 72000
=> x = 24000
Hence, A's investment = Rs. 27000
B's investment = Rs. 21000
C's investment = Rs. 24000
Ratio of the capitals of A, B and C
= 27000 : 21000 : 24000
= 9 : 7 : 8
A's share = Rs. [(7/24) Ã— 8640] = Rs. 2520
Answer: Option B
Answer: (B) Rs. 2520
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10 (B + G) is ?
(A) Equal to 3
(B) Less than 3
(C) More than 3
(D) Less than 1/3
(E) none of these
Rationale: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10
ANSWER:E
Answer: (E) none of these
Question: If x is an even integer, which of the following must be an odd integer?
(A) 3x/2
(B) [3x/2] + 1
(C) 3x^2
(D) [3x^2]/2
(E) [3x^2/2] + 1
Rationale: x is E (even) and therefore x^2 is E.
3x^2 is E, as it is O*E
Therefore, 3x^2/2 will be E. (since x is integer, x^2 > 2)
If you add 1 to an E number, you will always get odd.
Hence, E is the answer.
Answer: (E) [3x^2/2] + 1
Question: 2 minute is taken to travel the diagonal of square field at 3km/hour.calculate the area of field?
(A) 25 are
(B) 30 are
(C) 50 are
(D) 60 are
(E) 45 are
Rationale: speed of man=[3*5/18] m/sec.=5/6 m/sec., distance travel in 2 minute={5/6*2*60} m.=100 m.
diagonal of square field=100 m
area of field=1/2*diagonal^2=[1/2*100*100] sq.m=5000 sq.m=5000/100=50 are(1 are=100 sq. m)
answer C
Answer: (C) 50 are
Question: An elephant fell into a wall of depth 20mts.Everyday it climbs 4mts but at the end falls by 2mts.Find the number of days it would take for the elephant to get out of the wall
(A) 7 days
(B) 9 days
(C) 8 days
(D) 10 days
(E) 11 days
Rationale: 4-2=2
2*8=16
16(8 days)+4(9th day)=20
8+1 =9 days
ANSWER:B
Answer: (B) 9 days
Question: Two different natural numbers are such that their product is less than their sum. One of the numbers must be
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Solution
Since 1. x<1+x, so one of the numbers is 1.
Answer A
Answer: (A) 1
Question: 1394 x 1394
(A) 1943236
(B) 1981709
(C) 18362619
(D) 2031719
(E) None of these
Rationale: 1394 x 1394 = (1394)2
= (1400 - 2)2
= (1400)2 + (6)2 - (6 x 1400 x 6)
= 1943236.
Answer: Option A
Answer: (A) 1943236
Question: The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre.
(A) 2399
(B) 3888
(C) 2999
(D) 5808
(E) 2888
Rationale: Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.40) = Rs. 5808.
Answer: D) 5808
Answer: (D) 5808
Question: The traffic lights at 3 different roads change after every 32 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
(A) 9:29:24
(B) 9:42:15
(C) 10:15:24
(D) 9:54:12
(E) 10:01:20
Rationale: LCM of 32,72,108 = 864 =14mnts 24sec
The lines will change every 14m 24sec
The light will change again after 9:15 AM is = 9:15+0:14:24 = 9:29:24
Answer is A
Answer: (A) 9:29:24
Question: Population of a city in 20004 was 1000000. If in 2005 there is anincrement of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at theend of the year 2007
(A) 974553
(B) 945343
(C) 996545
(D) 984534
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: A peanut farmer sells his peanuts through a distributor, which take a commission of 17% of the price set by the farmer. The distributor obtains the product from a farmer at the price of $15 per peanut pound. What is the price that the buyer observers if the distributor wants to maintain a 17% profit on the cost of each pound of peanuts sold?
(A) 21.15
(B) 21.2
(C) 21.25
(D) 21.3
(E) 21.35
Rationale: Farmer price = $15;The distributor wants to maintain a 17% profit on the cost of each peanut pound, thus he must get $15*1.17 = $17.55 after the distributor takes a commission of 17% of the final price --> (final price)*0.83 = $17.55 --> (final price) = $21.15Answer: A.
Answer: (A) 21.15
Question: 1, 8, 27, 64, 125, 216, (....)
(A) 354
(B) 392
(C) 343
(D) 245
(E) 275
Rationale: Explanation :
The pattern is 13, 23, 33, 43, 53, 63, etc
Hence, next number is 73 = 343
Answer : Option C
Answer: (C) 343
Question: How many numbers from 2 to 13 are exactly divisible by 2?
(A) A)2
(B) B)3
(C) C)5
(D) D)7
(E) E)6
Rationale: 2/2 = 1 and 13/2 = 6
6 - 1 = 5
5 + 1 = 6 Numbers.
Answer : E
Answer: (E) E)6
Question: On January 1, 2011, John invests 60% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 20% in Antarctic smallcaps. In 2011, largecaps rise 10%, midcaps rise 20%, and smallcaps rise 10% in the Antarctic stock market; however, in 2012, largecaps fall 10% and midcaps fall 10%, while smallcaps rise x% in Antarctica. If, on January 1, 2013, John has the same total amount of retirement savings as he did two years before, then x is between
(A) 10 and 20
(B) 20 and 30
(C) 30 and 40
(D) 40 and 50
(E) 50 and 60
Rationale: Pick a smart number for the total retirement savings John starts with—say, $1,000. (If you pick $100, you’ll wind up needing to track decimals, so give yourself more zeros to start with.)
Here are the starting values:
L = $600
M = $200
S = $200
Apply the first year’s changes, so that you have these numbers on 1/1/2012:
Newer L = $600 + 10% = $660
Newer M = $200 + 20% = $240
Newer S = $200 + 10% = $220
Now apply the second year’s changes to L and M:
Newest L = $660 – 10% = $660 – $66 = $594
Newest M = $240 – 10% = $240 – $24 = $216
Add these to get $810. So the newest S must be $1,000 (the target final total of John’s retirement savings) minus $810, $190
The dollar change in S from 1/1/12 to 1/1/13 is $220 – $30 = $190. So the question is this: what percent change does $190 represent, from a starting point of $220? Since $220 is a nasty divisor, switch to benchmarks:
10% of $220 = $22.
So 20% is just double that, or $44.
And so on.
From this $30 lies between $22 and $44
The correct answer is A.
Answer: (A) 10 and 20
Question: If sin x + cos x =
1/2
, then what is the value of sin-3- x + cos-3-x?
(Suggestion: Do not nd the individual values of sin x and cos x.)
(A) 1 /2
(B) 3/ 4
(C) 9 /16
(D) 5/ 8
(E) 11/ 16
Rationale: Since sin x + cos x = 1=2, we get
1
4
= (sin x + cos x)2 = sin2 x + 2 sin x cos x + cos2 x = 1 + 2 sin x cos x:
It follows that sin x cos x = 􀀀3=8. Thus,
sin3 x + cos3 x = (sin x + cos x)(sin2 x 􀀀 sin x cos x + cos2 x) =
1/21 +
3/8 =
11/16
correct answer E
Answer: (E) 11/ 16
Question: In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 10% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
(A) a) 50%
(B) b) 53%
(C) c) 54%
(D) d) 55%
(E) e) 57%
Rationale: Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=57%
E
Answer: (E) e) 57%
Question: If k is an integer and 0.00010101 x 10^k is greater than 100, what is the least possible value of k?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 0.00010101 * 10^k > 100
We need to move the decimal point to the right 6 places to get 101.01
This is equivalent to multiplying by 10^6.
The answer is D.
Answer: (D) 6
Question: 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
(A) 12
(B) 15
(C) 18
(D) 47
(E) 4
Rationale: Explanation :
Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
ANSWER:E
Answer: (E) 4
Question: When positive integer x is divided by positive integer y, the remainder is 6. If x/y = 96.15, what is the value of y?
(A) 96
(B) 75
(C) 40
(D) 25
(E) 12
Rationale: by the definition of a remainder, the remainder here is equal to 6/y. the remainder in decimal form is given as .15
therefore, 6/y = .15
solve for y and get 40.
C
Answer: (C) 40
Question: Fifty percent of the subscribers to newspaper X are corporate managers and, of these, 30 percent are in the financial field. If 40 percent of the subscribers who are corporate managers in the financial field are money managers, how many of the newspaper's 25000 subscribers are corporate money managers in the financial field?
(A) 1,500
(B) 3,000
(C) 3,750
(D) 7,500
(E) 8,750
Rationale: Total Subscribers : 25k. Out of these, # of Corporate Managers = 12.5k. Out of these , 30 % are in financial field = 3.75k.
Thus, we have 3.75k Corporate managers, who are in financial field, and 40% of these are money managers = 1.5k
ANSWER:A
Answer: (A) 1,500