mathewhe/aqua_rat huggingface dataset:
Question: a man can row 16 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
(A) 8 km/hr.
(B) 6 km/hr.
(C) 9 km/hr.
(D) 15 km/hr.
(E) 11 km/hr.
Rationale: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=16 or x=8.
Rate upstream=8 km/hr,rate downstream=24 km/hr.
Hence,rate of stream=1/2(24-8)km/hr=8 km/hr.
Answer is A.
Answer: (A) 8 km/hr.
Question: If 7a = 2b = 15, then 42ab =
(A) 75
(B) 125
(C) 675
(D) 1100
(E) 1250
Rationale: 7a * 2b = 15 * 15 = 225
14 ab = 225
i.e. 42 ab = 675
Answer: Option C
Answer: (C) 675
Question: 6,9,15,27,51, (...)
(A) 44
(B) 86
(C) 12
(D) 99
(E) 64
Rationale: 6
6Ã— 2 - 3 = 9
9 Ã— 2 - 3= 15
15 Ã— 2 - 3 = 27
27 Ã— 2 - 3 = 51
51 Ã— 2 - 3 = 99
Answer is D
Answer: (D) 99
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 77 sec
(B) 12 sec
(C) 55 sec
(D) 43 sec
(E) 99 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: B
Answer: (B) 12 sec
Question: In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent of his family’s total income?
(A) 15%
(B) 17%
(C) 24%
(D) 30%
(E) 33%
Rationale: Lets suppose the Total Family income in Feb = 100x
Wilson's earning in Feb = 40% of 100x = 40x
Earnings of remaining family in Feb = 100x - 40x = 60x
Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x
Earnings of remaining family in March = Earnings of remaining family in Feb = 60x
Thus Wilson's earning as % of Total family income in March = 30x/ (30+60)x = 30x/90x = 33.33%
Thus Answer is E
Answer: (E) 33%
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 99 true?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Answer C
(a+b)(a-b)=99
3 cases For (a+b), (a-b)
99, 1
33, 3
11, 9
Answer B
Answer: (B) 3
Question: An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 12%. How much will an air-conditioning unit cost in November?
(A) $442
(B) $470
(C) $472
(D) $484
(E) $491
Rationale: if its previous November(before discount) then price is $470.
but if its November of next year then
16% discount on $470=470(1-16/100)=$394.8
again a corrected raised price of 12% over $394.8=394.8(1+12/100)=442.176~$4442
Ans A
Answer: (A) $442
Question: Molly can do a task in 15 days while Sandy can do the task in 10 days. How many days will it take to complete the task if both work together?
(A) 6
(B) 7
(C) 7.5
(D) 8
(E) 9
Rationale: Each day, Molly can do 1/15 of the task.
Each day, Sandy can do 1/10 of the task.
Each day, they can do 1/15 + 1/10 = 1/6 of the task.
The task will be completed in 6 days.
The answer is A.
Answer: (A) 6
Question: Miguel is 46 years old. He is 2 years older than twice his son’s age. Find the age of his son.
(A) 11years
(B) 12years
(C) 15years
(D) 19years
(E) 22years
Rationale: sons age=x
46-2x=2
x=22years
ANSWER:E
Answer: (E) 22years
Question: If p and q are the two digits of the number 653pq such that this number is divisible by 80, then p+q is equal to :
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: Since 653xy is divisible by 5 as well as 2, so y = 0.
Now, 653x0 must be divisible by 8.
So, 3x0 must be divisible by 8. This happens when x = 2
x + y = (2 + 0) = 2.
ANSWER:A
Answer: (A) 2
Question: A and B start a business with Rs.6000 and Rs.2000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:5
(B) 3:4
(C) 3:9
(D) 3:1
(E) 3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 2000 => 3:1,Answer: D
Answer: (D) 3:1
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for one year, compounding done annually?
(A) 9688
(B) 9687
(C) 9685
(D) 9682
(E) 8800
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}1 = Rs.8800
Answer:E
Answer: (E) 8800
Question: A, B and C have Rs.1000 between them, A and C together have Rs.700 and B and C Rs.600. How much does C have?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: A+B+C = 1000
A+C = 700
B+C = 600
--------------
A+B+2C = 1300
A+B+C = 1000
----------------
C =300
ANSWER:C
Answer: (C) 300
Question: Smith can do a work in 15 days while Johnson can do it in 25 days. How long will they take if both work together?
(A) 3 4/9 days
(B) 8 4/9 days
(C) 9 3/8 days
(D) 6 3/8 days
(E) 7 3/8 days
Rationale: Explanation:
1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Answer: C
Answer: (C) 9 3/8 days
Question: A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
(A) 145°
(B) 150°
(C) 155°
(D) 155°
(E) None
Rationale: Sol.
Angle traced by hour hand in 12hrs = 360°
Angle traced by hour hand in 5hrs 10 min. i.e. 31/6 hrs.
= (360/12 x 31/6)° = 155°
Answer C
Answer: (C) 155°
Question: 19 men and 12 boys finish a job in 3 days, 7 men and 7 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
(A) 03
(B) 05
(C) 12
(D) 17
(E) 12
Rationale: 19 M + 12 B ----- 03 days
13 M + 13 B ------- 10 days
18 M + 18 B -------?
247 M +156 B = 234 M +234 B
78 B = 13 M => 1 M = 6 B
114 B + 12 B = 126 B ---- 03 days
108 B + 18 B = 126 B -----? => 03 days
Answer: A
Answer: (A) 03
Question: The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is:
(A) 12
(B) 24
(C) 84
(D) 48
(E) 42
Rationale: Let the numbers be x and 4x. Then, x * 4x = 84 * 21 x2 = (84 * 21)/4 = x = 21.
Hence, larger number = 4x = 84.
ANSWER:C
Answer: (C) 84
Question: If an integer w is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that w(w + 1)(w + 2) will be divisible by 8?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: for w Total numbers 8*12
There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))
and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))
The answer 5/8 -> D
Answer: (D) 5/8
Question: Rs.12320 were divided among W, X & Y in such a way that W had Rs.640 more than X and Y had Rs 480 more than X . How much was Xâ€™s share?
(A) Rs.4590
(B) Rs.4610
(C) Rs.4620
(D) Rs.4630
(E) Rs.4640
Rationale: Let X gets Rs x. Then We can say W gets Rs (x + 640 ) and Y gets Rs ( x + 560) .
x + 640 + x + x + 1120 = 12320
3x = 10560
x = 3520 .
Câ€™s share = Rs ( 3520+1120 ) = Rs.4640
E
Answer: (E) Rs.4640
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
(A) 50
(B) 56
(C) 70
(D) 60
(E) 80
Rationale: Let the actual distance travelled be x km.
Then,x/10=(x + 20)/14
14x = 10x + 200
4x = 200
x = 50 km.
Answer:A
Answer: (A) 50
Question: n how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
(A) 25401600
(B) 25401800
(C) 254016200
(D) 26401600
(E) 27401600
Rationale: There are 12 words in letter PERMUTATIONS. Out of which T is repeated twice.
Now first we need to see how many ways we can make word with 4 letter between P and S.
Except P and S there are total of 10 letters, so number of way of selecting them = 10C4 = 210
Also note that question is asking to place exactly 4 words between P and S, but does not tells you if P has to be the first letter of S has to be the first letter. So In all the above combinations, we can rotate the position of P and S.
So total way = 210*2 = 420
The selected 4 letters can be rotated between P and S in = 4! ways
So total ways = 420 * 4!
Consider this 6 letter chunk (P, S, and 4 letter between them) as 1 letter.
Remaining letters are 6. So in total we have 7 letters, which can be arranged in 7! ways.
So total number of ways = 7! * 420 * 4!
Now since letter T was repeated twice, we should divide the above result by 2!.
So Total number of ways = 7! * 420 * 4! / 2! = 25401600 A
Answer: (A) 25401600
Question: There are 50 people and 3 clubs M, S, and Z in a company. 14 people joined M, 16 people joined S and 9 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not
join any club?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Answer E.
key is 'atmost' here.
so 14 people joined M.
16 people joined S and 9 people joined Z. to get maximum people who did not join any club, 9 people who joined Z are among 14 people who joined S.
so 16+14 = 30
50-30 = 20
Answer: (E) 20
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 22.55%. What would have been the percentage of profit earned if no discount was offered?
(A) 60%
(B) 29%
(C) 39%
(D) 56%
(E) 73%
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 122.55
Let marked price be Rs. x. Then, 95/100 x = 122.55
x = 12255/95 = Rs. 129
Now, S.P. = Rs. 129, C.P. = Rs. 100
Profit % = 29%.
Answer: B
Answer: (B) 29%
Question: On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $80,000?
(A) 15
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: x- interest rate
80.000= 10.000 (1+x)^year
=> 8=(1+x)^year
40.000=10.000 . (1+x)^12
=> 4= (1+x)^12
=>2= (1+x)^6
=> 8 = (1+x)^ 18
So, after 18 years, the total value of the investment plus interest will increase to $80,000.
ANSWER:C
Answer: (C) 18
Question: An Olympic diver received the following scores: 2, 4, 6, 8. The standard deviation of her scores is in which of the following ranges?
(A) 4.01 to 4.99
(B) 1.01 to 1.99
(C) 3.01 to 3.99
(D) 2.01 to 2.99
(E) 5.01 to 5.99
Rationale: 2+4+6+8/4=5
∣2-5∣^2 =3^2 = 9
∣4-5∣^2 =1^2 = 1
∣6-5∣^2 =1^2 = 1
∣8-5∣^2 =3^2 = 9
sqrt 20/4 =2.24
Answer : D
Answer: (D) 2.01 to 2.99
Question: According to a survey conducted in two cities, A and B, 64% of the population is happy with the new president. If the ratio of the city A population to the city B population is 3:2 and the percentage of city A residents who are happy with the president is 70%, what percentage of city B population is happy with the president?
(A) 30%
(B) 50%
(C) 25%
(D) 55%
(E) 62%
Rationale: A/B = 3/2 = x suppose
that for A=3x
B=2x
Total A+B=5x
Now 64% is happy with new president, 64%*(5x) =3.2x is happy with new present out of total population of A & B
now 70% of A is happy with new pres, so 70%*(3x) = 2.1x
Total happy people are 3.2x
so B=3.2x-2.1x=1.1x is happy
Now B's population is 2x
1.1x is 55% of total population of B
Answer : D
Answer: (D) 55%
Question: A man swims downstream 96 km and upstream 40 km taking 8 hours each time; what is the speed of the current?
(A) 3.5 kmph
(B) 1.5 kmph
(C) 13 kmph
(D) 6.5 kmph
(E) 7:3kmph
Rationale: Explanation:
96 --- 8 DS = 12
? ---- 1
40 ---- 8 US = 5
? ---- 1 S = ?
S = (12 - 5)/2 = 3.5
Answer: Option A
Answer: (A) 3.5 kmph
Question: What is the area of a square field whose sides have a length of 11 meters?
(A) 225 sq m
(B) 205 sq m
(C) 121 sq m
(D) 167 sq m
(E) 156 sq m
Rationale: 11 * 11 = 121 sq m
The answer is C.
Answer: (C) 121 sq m
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 395 km of the tour is:
(A) 31.11 km/hr
(B) 87.8 km/hr
(C) 71.11 km/hr
(D) 36 km/hr
(E) 71 km/hr
Rationale: Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 395 x 2/9 = 87.8 km/hr.
Answer : B.
Answer: (B) 87.8 km/hr
Question: A number when divided by a divisor leaves a remainder of 23. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 12
(B) 13
(C) 35
(D) 36
(E) 59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+23
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 36
as D is also integer and 36 is a prime number, the D should be 36 to satisfy the above equation.
Hence answer is 'D'
Answer: (D) 36
Question: Stacy has a 33 page history paper due in 3 days. How many pages per day would she have to write to finish on time?
(A) 9
(B) 8
(C) 11
(D) 8.5
(E) 6
Rationale: 33/3=11
Answer : C
Answer: (C) 11
Question: The population of a town has increased from 133575 to 138918. The percent increase in population is :
(A) 2.5
(B) 3
(C) 4.5
(D) 4
(E) 3.5
Rationale: (133575-138918)/138918*100=4
ANSWER:D
Answer: (D) 4
Question: How many three digit even numbers do not use any digit more than once
(A) None of these
(B) 2160
(C) 2240
(D) 2460
(E) 2520
Rationale: The Way i solved it is
A B C ( hundreds, tens, units)
C can be 0 2 4 6 8 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 7 * 8 * 5 = 280
Ans :A
Answer: (A) None of these
Question: A car traveled from San Diego to San Francisco at an average speed of 48 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
(A) 24.
(B) 32.
(C) 36
(D) 42.
(E) 44.
Rationale: Let the time taken be = x
One way distance = 48x
Total distance traveled = 2 * 48x = 96x
Total time taken = x + 2x = 3x
Average speed = 96x/3x = 32
Answer: B
Answer: (B) 32.
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 22
(B) 28
(C) 20
(D) 82
(E) 34
Rationale: M = 15
S = 5
DS = 15 + 5 = 20.Answer:C
Answer: (C) 20
Question: emblem is coded as 216;
crude is coded as 125
bat will be ?
(A) 45
(B) 32
(C) 27
(D) 56
(E) 64
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
bat = 3^3 =27
ANSWER:C
Answer: (C) 27
Question: What number should replace the question mark? 3, 30, 11, 24, 19, 18, ---?
(A) 24
(B) 22
(C) 27
(D) 25
(E) 28
Rationale: Answer: C
3, 30, 11, 24, 19, 18, 27?
There are two alternate sequences: +8 and -6.
Answer: (C) 27
Question: The price of an item is discounted 3 percent on day 1 of a sale. On day 2, the item is discounted another 3 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 85.1%
(B) 86.9%
(C) 87.3%
(D) 88.8%
(E) 89.5%
Rationale: Let initial price be 100
Price in day 1 after 3% discount = 97
Price in day 2 after 3% discount = 94.09
Price in day 3 after 10% discount = 84.68
So, Price in day 3 as percentage of the sale price on day 1 will be = 84.68/97*100 => 87.3%
Answer will definitely be (C)
Answer: (C) 87.3%
Question: If a and b are integers and (a*b)^5 = 48y, y could be:
(A) 8
(B) 16
(C) 162
(D) 144
(E) 100
Rationale: Distribute the exponent.
a^5 * b^5 = 48 y
Find the prime factorization of 48. This is 2^4 *3^1.
We need 2^1*3^4 (or some other power of 3 that will give us a multiple of 3^5 as our second term).
3^4*2 = 81*2= 162
The answer is C.
Answer: (C) 162
Question: The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
(A) 16
(B) 12
(C) 20
(D) 24
(E) 35
Rationale: Side of first square = (40/4) = 10 cm;
Side of second square = (32/4)cm = 8 cm.
Area of third square = [(10) 2 - (8) 2] cm2 = (100 - 64) cm2 = 36 cm2.
Side of third square = (36)(1/2) cm = 6 cm.
Required perimeter = (6 x 4) cm = 24 cm.
Ans: D
Answer: (D) 24
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 21 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 877 m
(B) 225 m
(C) 167 m
(D) 887 m
(E) 265 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 21)m = 315 m. Let the length of the platform be x meters. Then, (x + 315)/36 = 15
==> x + 315 = 540 ==> x
= 225 m.
Answer: B
Answer: (B) 225 m
Question: 7 3/4 + 7 2/17 - 9 1/15=?
(A) 7 719/1020
(B) 9 817/1020
(C) 9 719/1020
(D) 5 817/1020
(E) None of them
Rationale: Given sum=7+3/4+7+2/17-(9+1/15)
=(7+7-9)+(3/4+2/17-1/15)
=5+(765+120-68/1020
=5 817/1020
Answer is D
Answer: (D) 5 817/1020
Question: If daily wages of a man is five times to that of a woman, how many men should work for 20 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
(A) 12
(B) 14
(C) 16
(D) 8
(E) 20
Rationale: Explanation :
Wages of 1 woman for 1 day = 21600/40Ã—30
Wages of 1 man for 1 day = 21600Ã—5/40Ã—30
Wages of 1 man for 20 days = 21600Ã—5Ã—20/40Ã—30
Number of men = 14400/(21600Ã—5Ã—20/40Ã—30)=144/(216Ã—100/40Ã—30)=8
Answer : Option D
Answer: (D) 8
Question: Convert 300 miles into meters?
(A) 784596
(B) 845796
(C) 804670
(D) 482802
(E) 864520
Rationale: 1 mile = 1609.34 meters
300mile = 300*1609.34 = 482802 meters
Answer is D
Answer: (D) 482802
Question: The average of 11 results is 55, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: 1 to 11 = 11 * 55 = 605
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 605 = 4
ANSWER:A
Answer: (A) 4
Question: 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is ?
(A) 7 years
(B) 5 years
(C) 3 years
(D) 4 years
(E) 2 years
Rationale: Explanation:
Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be years.
Then, age of the elder child = years.
So,
Age of younger child = 3 years.
Answer: C
Answer: (C) 3 years
Question: Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?
(A) 8 min 15 sec
(B) 7 min 15 sec
(C) 6 min 15 sec
(D) 5 min 15 sec
(E) 4 min 15 sec
Rationale: Explanation:
Part filled in 3 minutes =
3∗(1/12+1/15)=3∗9/60=9/20
Remaining part =1−9/20=11/20
=>1/15:11/20=1:X
=>X=11/20∗15/1
=>X=8.25mins
So it will take further 8 mins 15 seconds to fill the bucket.
Option A
Answer: (A) 8 min 15 sec
Question: What is the speed of the stream if a canoe rows upstream at 6km/hr and downstream at 12km/hr
(A) 1 kmph
(B) 4 kmph
(C) 3 kmph
(D) 2 kmph
(E) 1.9 kmph
Rationale: Sol.
Speed of stream = 1/2(12 -6) kmph = 3 kmph.
Answer C
Answer: (C) 3 kmph
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 68 with him, what was the average amount with the group before his joining the group?
(A) s.13
(B) s.11
(C) s.15
(D) s.22
(E) s.12
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 68. So, the amount with remaining 6 people = 140 - 68 = Rs. 72
The average amount with them = 72/6 = Rs.12.
Answer:E
Answer: (E) s.12
Question: The average expenditure of a man for the first five months is Rs.360 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
(A) Rs.140
(B) Rs.150
(C) Rs.250
(D) Rs.350
(E) none
Rationale: Explanation:
Total income = Rs.(360Ã—5+130Ã—7+290)=Rs.3000
Average monthly income
= Rs. (3000/12)=Rs.250
Correct Option: C
Answer: (C) Rs.250
Question: Find the ratio between whole surfaces of a sphere and a hemisphere?
(A) 4:9
(B) 4:3
(C) 4:5
(D) 4:0
(E) 4:1
Rationale: Explanation:
4 πr2 : 3 πr2 => 4:3
Answer: Option B
Answer: (B) 4:3
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 360 m long?
(A) 30 Seconds
(B) 22 Seconds
(C) 41 Seconds
(D) 24 Seconds
(E) 29 Seconds
Rationale: 30 Seconds
Distance travelled = 140 + 360m = 500m
Speed = 60 * 5/8 = 50/3m
Time = 500 * 3/50 = 30 Seconds
ANSWER A
Answer: (A) 30 Seconds
Question: A boat running up stram takes 6 hours to cover a certain distance, while it takes 7 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
(A) 2 : 3
(B) 5 : 6
(C) 4 : 5
(D) 13 : 1
(E) 8 : 1
Rationale: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
6(x+y) = 7(x-y)
6x+6y = 7x-7y
13y = x
13y = x
x/y = 13/1
13 : 1
Answer: Option D
Answer: (D) 13 : 1
Question: There are some people in party, 1/3rd left the party . Then 2/5th of the remaining left the party , then 2/3rd of the remaining left the party . At last 10 were remaining . How many people were in total ?
(A) 45
(B) 27
(C) 28
(D) 26
(E) 75
Rationale: Sol:
45
If x persons were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 10
x×2/3 × 3/5 × 1/3 = 10
x = 75
Answer:E
Answer: (E) 75
Question: How long will it take a sum of money invested at 8% p.a. S.I. to increase its value by 80%?
(A) 12 years.
(B) 11 years.
(C) 8 years.
(D) 10 years.
(E) 9 years.
Rationale: Sol.
Let the sum be x. Then, S.I. = 80% of x = 4x/5; Rate = 8%.
âˆ´ Time = [100 * 2x/5 * 1/x*8 = 10 years.
Answer D
Answer: (D) 10 years.
Question: What least number must be subtracted from 9671 so that the remaining number is divisible by 2?
(A) 3
(B) 1
(C) 16
(D) 11
(E) 15
Rationale: On dividing 9671 by 2, we get remainder = 1.
Required number be subtracted = 1
ANSWER:B
Answer: (B) 1
Question: If x and y are integers such that x^2-4x+2y+6=2x^2-5x+y-6, we can deduce that y is
(A) not an even
(B) an even
(C) a perfect square
(D) an odd
(E) a prime
Rationale: x^2 - 4x + 2y + 6 = 2x^2 - 5x + y - 6
y = x^2 - x - 12
y = (x-4)(x+3) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B.
Answer: (B) an even
Question: If 5th March, 2009 is Tuesday, what was the day of the week on 5th March, 2008?
(A) Sunday
(B) Saturday
(C) Tuesday
(D) Wednesday
(E) Monday
Rationale: Solution
The year 2008 is a leap year. So, it has 2 odd days.
But, Feb 2008 not included because we are calculating from March 2008 to March 2009. So it has 1 odd day only.
The day on 5th March, 2009 will be 1 day beyond the day on 5th March, 2008. Given that, 5th March, 2009 is Tuesday.
5th March, 2008 is Monday (1 day before to 5th March, 2009)
Answer E
Answer: (E) Monday
Question: If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)
(A) 0.25
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Rationale: (a-b)-(c-d)=6 and (c-d)-(a+b)=3
(a-c)-(b+d)=6 and (c-a)-(b+d)=3
(b+d)= (a-c)-6 and (b+d)=3-(c-a)
2(a-c)=3
(a-c)=1.5
ANSWER B 1.5
Answer: (B) 1.5
Question: If x is less than y by 50% then y exceed x by:
(A) 33.33%
(B) 100%
(C) 75%
(D) 66.66%
(E) None of these
Rationale: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 50(100-50)*100
=100%
ANSWER:B
Answer: (B) 100%
Question: Given that a/b < 1, and both a and b are positive integers, which one of the following must be greater than 1?
(A) a/b^2
(B) a^2/b
(C) a^2/b^2
(D) b/a
(E) √(a/b)
Rationale: Since a/b is a fraction b must always be > 1
Given -
Which one of the following must be greater than 1
We can get the result one only when the denominator in a/b ( Which is less than 1 ) becomes numerator..
Among the given options only (D) has the required characteristic we are looking for...
Hence answer will be (D)
Answer: (D) b/a
Question: What is the HCF of 2/3, 4/9 and 6/5
(A) 7/45
(B) 2/45
(C) 4/15
(D) 8/45
(E) 9/45
Rationale: Explanation:
HCF of Fractions = HCF of Numerators/LCM of Denominators
= (HCF of 2, 4, 6)/(LCM of 3, 9, 5) = 2/45
Answer: Option B
Answer: (B) 2/45
Question: P, Q and R have Rs.9000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
(A) Rs.3000
(B) Rs.3600
(C) Rs.2400
(D) Rs.4000
(E) None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(9000 - r) => 3r = 18000 - 2r
=> 5r = 18000 => r = 3600.
ANSWER:B
Answer: (B) Rs.3600