mathewhe/aqua_rat huggingface dataset:
Question: One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met?
(A) 38.07
(B) 40
(C) 42
(D) 39
(E) 40.07
Rationale: Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows
9t + 8(t + 1) = 80
9t + 8t + 8 = 80
17t = 72
T = 4.23 (hours)
Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is A.
Answer: (A) 38.07
Question: Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 33 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
(A) 1/3
(B) 3
(C) 27/8
(D) 9
(E) 12
Rationale: In 15 mins, Timothy travels=9/4 miles.
Now, let his mother takes x hours to reach him, traveling at 31mph.
So, 33x=9x+9/4
x=3/32 hrs.
Thus, the distance traveled by his mother to reach= 36*3/32=27/8 miles. Ans C
Answer: (C) 27/8
Question: There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?
(A) 20
(B) 30
(C) 50
(D) 60 peacocks
(E) 80
Rationale: Explanation:
Let x and y be the number of deer and peacocks in the zoo respectively. Then,
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
Answer: D
Answer: (D) 60 peacocks
Question: What is the two-digit number? I. Sum of the digits is 7. II. Difference between the number and the number obtained by interchanging the digits is 9. III. Digit in the ten's place is bigger than the digit in the unit's place by 1.
(A) I and II
(B) II and III
(C) I and III
(D) I and II as well as I and III
(E) All
Rationale: Explanation:
Let the tens and units digit be x and y respectively.
I. x + y = 7.
II. (10x + y) - (10y + x) = 9 x - y = 1.
III. x - y = 1.
Thus, I and II as well as I and III give the answer.
Correct answer is (D).
Answer: (D) I and II as well as I and III
Question: Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 3000 Km?
(A) 100.
(B) 25.
(C) 30.
(D) 150.
(E) 50.
Rationale: Total distance= Distance travelled by A +Distance travelled by car B
Distance= speed*time
Distance of A= 3x * 6
Distance of B= x*2
(3x * 6) + (x*2) = 3000
x= 150 KM/hr
D is the answer
Answer: (D) 150.
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?
(A) 1/4
(B) 3/4
(C) 4/7
(D) 4/11
(E) 5/7
Rationale: Total number of cases = 6*6 = 36
Favourable cases = [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27
So Probability = 27/36 = 3/4
B)
Answer: (B) 3/4
Question: 55th word of SHUVANK in dictionary??
(A) AHSNKUV
(B) AHNKSVU
(C) AHNKUSV
(D) AHNKUVS
(E) AHNKUVV
Rationale: First of all write letters in the alphabetical order : A,H,K,N,S,U,V
Then we fix the in order AHK_ _ _ _=> we get 4! means 24 words.
After Next letter in alphabetical order is AHN_ _ _ _=> we get 4! means 24 words
Now we get total 48 words.. Then
In order to Next word is AHSK_ _ _ => Filling this we can fill in 3! Ways means 6.
Now we get total 54 words then next Word is AHSNKUV
ANSWER:A
Answer: (A) AHSNKUV
Question: If the price of a book is first decreased by 25% and then increased by 20%, then the decrease in the price will be?
(A) 20%
(B) 10%
(C) 25%
(D) 18%
(E) 30%
Rationale: Let the original price be $100
New final price = 120% of (75% of $100)
= 120/100 * 75/100 *100 = $90
Decrease is 10%
Answer is B
Answer: (B) 10%
Question: A person covers a distance in 21 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
(A) 18 m/s
(B) 4 m/s
(C) 14 m/s
(D) 10 m/s
(E) 5 m/s
Rationale: Explanation:
T = 21 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
21 x (10/3) = 5x
x = 14 m/s
Answer: Option C
Answer: (C) 14 m/s
Question: Barbara has 10 shirts and 8 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
(A) 41
(B) 66
(C) 36
(D) 70
(E) 74
Rationale: Total no of combinations available is= 10 shirts X 8 pants = 80
Eliminate the 2shirts X 3 pants combo = 6 which gives.......>> 80-6=74
ANSWER: D
Answer: (D) 70
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 960gm. for a kg.His gain is …%.
(A) 4.16%
(B) 5.36%
(C) 4.26%
(D) 6.26%
(E) 7.26%
Rationale: His percentage gain is 100*40/960 as he is gaining 40 units for his purchase of 960 units.
so 4.16%.
ANSWER:A
Answer: (A) 4.16%
Question: The average age of a group of persons going for picnic is 16 years. Twelve new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
(A) 5
(B) 10
(C) 12
(D) 40
(E) 50
Rationale: Solution
Let the initial number of persons be x. Then
16x + 12 x 15 = 15.5(x+20)
= 0.5x = 6
x = 12.
Answer C
Answer: (C) 12
Question: What percent is 36 paisa's of 12 rupees?
(A) 2 %
(B) 3 %
(C) 4 %
(D) 5 %
(E) 6 %
Rationale: 12 Rupees = 1200 paisa's
36/1200 × 100 = 3/12
12/3 = 3 %
B
Answer: (B) 3 %
Question: 9C2 + 9C3 +10C4=?
(A) 300
(B) 330
(C) 360
(D) 390
(E) 410
Rationale: 36+84+210=330
ANSWER:B
Answer: (B) 330
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 10
(B) 15
(C) 17
(D) 24
(E) 26
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
(A) 60.5
(B) 35.5
(C) 25.5
(D) 62
(E) 62.5
Rationale: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
New capacity of bucket =(2/5)x
Required number of buckets =	25x/(2x/5)
= 25x * 5/2x
=125/2
= 62.5
Answer is E.
Answer: (E) 62.5
Question: In 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each, how many pumps will raise 2030 tons of water in 12 days of 11 hrs each?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 22
Rationale: Explanation:
pumps work time
12 1218 99
x 2030 132
=> 1218/(912*99) = 2020/(x × 132)
=> x = 15 pumps
Answer: Option B
Answer: (B) 15
Question: In the City 45% of the population lived in the East at the Beginning of the Year and the rest of the City lived in the West. During the Same Year, the population of City grew by 5.0%. If the population in the West grew by 2.5%, by how much did the population grow in the remaining side?
(A) 5.9%
(B) 2.5%
(C) 5.0%
(D) 8.2%
(E) 7.5%
Rationale: Ratio of population in City = East:West :: 45%:45% = 1:1
Mean growth = 5%
West Growth: 2.5%
East Growth = ??
East-------------Average--------------West
? __(1n)_____5.0%_____(1n)_____2.5%
Since:
2.5+1n=5
n=2.5
Therefore:
East=5+1n
East=5+2.5
That is the population grew in East Side of the town is 7.5%
Answer: (E) 7.5%
Question: What is the difference between the C.I. on Rs. 7000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) s.2.04
(B) s.2.08
(C) s.2.02
(D) s.2.86
(E) s.2.42
Rationale: C.I. when interest is compounded yearly
= [7000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 7000 * 26/25 * 51/50 = Rs. 7425.6
C.I. when interest is compounded half-yearly
= [7000 * (1 + 2/100)2]
= (7000 * 51/50 * 51/50 * 51/50)
= Rs. 7428.46 Difference
= (7428.46 - 7425.6)
= Rs.2.86.
Answer: D
Answer: (D) s.2.86
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m^3) is:
(A) 2130
(B) 3620
(C) 4512
(D) 5620
(E) 5120
Rationale: Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m^3.
ANSWER E
Answer: (E) 5120
Question: Weights of two friends Ram and Shyam are in the ratio 3:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
(A) 18%
(B) 10%
(C) 21%
(D) 16%
(E) None
Rationale: Solution:
given ratio of Ram and Shayam's weight = 3:5
Hence, (x-15)/(15-10) = 3/5
Or, x = 18%.
Answer: Option A
Answer: (A) 18%
Question: The average age of 20 students in a class is 5years. If teacher's age is also included then average increases 1year then find the teacher's age?
(A) 28
(B) 24
(C) 20
(D) 22
(E) 18
Rationale: Total age of 50 students = 20*5 = 100
Total age of 51 persons = 20*6 = 120
Age of teacher = 120-100 = 20years
Answer is C
Answer: (C) 20
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 108. What was the number he chose?
(A) 123
(B) 267
(C) 277
(D) 267
(E) 120
Rationale: Let xx be the number he chose, then
2â‹…xâˆ’138=108
x=123
Answer:A
Answer: (A) 123
Question: 140 college students were asked in a survey if they preferred Windows or Mac brand computers. 80 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 50 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
(A) 25
(B) 10
(C) 50
(D) 60
(E) 75
Rationale: 140 = 80(Mac) + x(Window) + 50(both) => x=10
ANSWER:B
Answer: (B) 10
Question: If n is a positive integer such that
n!/(n-2)! = 342, find n.
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: We write n! = n*(n-1)(n-2!)
Therefore
n!/(n-2)! = n(n-1)*(n-2)!/(n-2)! = n(n-1).
--> n(n-1) = 342
--> n^2 -n - 342 = 0
--> n^2- 19n +18n -342 = 0
--> n(n-19) +18(n -19) = 0
--> (n-19)(n+18) = 0
Therefore n -19 = 0; n +18 = 0;
(i.e) n =19 ; n = -18
We want positive integer. So, n=19.
ANSWER:C
Answer: (C) 19
Question: The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 19 positive perfect squares?
(A) 1,010
(B) 1,164
(C) 1,240
(D) 1,316
(E) 2,470
Rationale: First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.
Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.
Plug values of n = 19 and c = 1/2 into the equation and simplify to get the answer 2470.
Option E.
Answer: (E) 2,470
Question: A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
(A) 12%
(B) 10%
(C) 21%
(D) 15%
(E) 17%
Rationale: Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 20% on 140.
Profit=112-100
12%
answer A
Answer: (A) 12%
Question: The radius of a cone is 49 m, slant height is 35 m. Find the curved surface area?
(A) 5160
(B) 5390
(C) 6430
(D) 6720
(E) 7280
Rationale: Cone curved surface area = Ï€rl
22/7 Ã— 49 Ã— 35 = 154 Ã— 35 = 5390 m(power2)
Answer is B.
Answer: (B) 5390
Question: Amit Kumar invested an amount of 15,000 at compound interest rate of 10 pcpa for a period of two years. What amount will he receive at the end of two years?
(A) 18,000
(B) 18,500
(C) 17,000
(D) 17,500
(E) None of these
Rationale: Amount = 15000 (1 + 10⁄100)2
= 15000 × 11⁄10 × 11⁄10 = 18150
Answer E
Answer: (E) None of these
Question: At a certain amateur bands rock show the ratio of freaks to nerds to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling "rock on!", what are the chances that the next person who yells "rock on!" will be a geek?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: the ratio of freaks to nerds to geeks is 1:2:3.
So, Assuming the number as x,2x and 3x for freaks , nerds and geeks respc.
Probability of next person being Geek = 3x/total
or 3x/6x= 1/2. Hence , C.
Answer: (C) 1/2
Question: The product of n^2 consecutive positive integers is always divisible by
(A) n^2 -1
(B) (n+1)!
(C) 2n +1
(D) n^2 + 1
(E) n!
Rationale: Plug in some vlues and check -
Product of first 2 number is 2*1
Product of first 3 number is 3*2*1
Product of first 4 number is 4*3*2*1
Product of first 5 number is 5*4*3*2*1
So, The product of first n natural numbers is always divisible by n! , answer will be (A)
Answer: (A) n^2 -1
Question: If a boat goes 5km upstream in 25 minutes and the speed of the stream is 7 kmph, then the speed of the boat in still water is ?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: Rate upsteram =(5/25*60)kmph=12kmph.
speed of the stream =7kmph let speed in still water be xkm/hr. then speed upstream=(x-7)km/hr. x-7=12==>x=19km/hr Answer(B)
Answer: (B) 19
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6, 7 and 8 such that the numbers are divisible by 9?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 18,27, 36, 45, 54, 63, 72 ,81--- 8 Cases
Answer: option E
Answer: (E) 8
Question: Write 450,000,000,000 in scientific notation.
(A) 400.50 * 10 11
(B) 400.5 * 10 11
(C) 40.5 * 10 11
(D) 4.5 * 10 11
(E) 450.00 * 10 11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
450,000,000,000 = 4.5 * 100,000,000,000 = 4.5 * 10 11**
correct answer D
Answer: (D) 4.5 * 10 11
Question: The Racing magic takes 60 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Time taken by Racing magic to make one circle = 60 seconds
Time taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds
LCM of 90 and 60 seconds = 180 seconds
Time taken for them to meet at the starting point for the second time = 180 *2 =360 seconds= 6 mins
Answer B
Answer: (B) 6
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.2,10,000 earned at the end of 3 years from the start of the business in 1999 ?
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.75,000
(E) None of these
Rationale: Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(21000x2/6) = Rs. 70,000. Answer C
Answer: (C) Rs.70,000
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) Rs.6727
(B) Rs.6735
(C) Rs.6721
(D) Rs.6725
(E) Rs.6729
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124)
= Rs.6725.
Answer: D
Answer: (D) Rs.6725
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 2500 resolutions?
(A) 1187 m
(B) 1704 m
(C) 2179 m
(D) 3520 m
(E) 4297 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 2500 resolutions.
= 2500 * 2 * 22/7 * 22.4
= 352000 cm
= 3520 m
Answer:D
Answer: (D) 3520 m
Question: The present population of a town is 500. Population increase rate is 10% p.a. Find the population of town before 2 years?
(A) 512
(B) 615
(C) 810
(D) 413
(E) 123
Rationale: P = 500
R = 10%
Required population of town = P/(1 + R/100)^T
= 500/(1 + 10/100)^2
= 500/(11/10)^2
= 413(approximately)
Answer is D
Answer: (D) 413
Question: 70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 23.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
(A) one
(B) two
(C) three
(D) four
(E) five
Rationale: The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-23,4=76,6. There are only two numbers below 76,6. The answer is B
Answer: (B) two
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
(A) 12 years
(B) 14 years
(C) 18 years
(D) 20 years
(E) 22 years
Rationale: Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 6 years = (x+ 6) = 20 years.. Answer: Option D
Answer: (D) 20 years
Question: In the third grade of Windblown School there are 108 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
(A) 0.
(B) 6.
(C) 8.
(D) 10
(E) 12
Rationale: One third of them failed the math test = 1/3 of 108 = 36. Passed in math test = 82.
And 1/6 failed that literature test = 18.
It is a possible scenario that these 18 (failed in literature) were the ones who passed the math test. So in this case, no one failed in both.
Hence A.
Answer: (A) 0.
Question: There are 4 more women than men on Centerville's board of education. If there are 14 members on the board, how many are women?
(A)  3
(B)  4
(C)  6
(D)  7
(E)  9
Rationale: Given: M=W-4 so, W+(W-4)=14 --> W=9.
Answer: E.
Answer: (E)  9
Question: One urn contains two pieces of candy{one green and one red. A second urn
contains four pieces of candy{one green and three red. For each urn, each piece of candy is
equally likely of being picked. You pick a piece of candy from each urn and eat the two chosen
candies.
If you eat exactly one piece of green candy, you draw a second piece of candy from the urn
still containing a green piece of candy. You now eat the candy you just chose. What is the
probability that you ate two pieces of green candy?
(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 5/8
Rationale: There are four possibilities for the rst round:
You pick a green piece of candy from each urn. (Probability 1/2*1/4=1/8)
You pick the green piece of candy from the rst urn and the red piece of candy from the
second. (Probability 1/2 * 3/4 = 3/8 :) You have a 1/3 chance of eating the green piece of candy
on the second round (since three pieces of candy remain in the second urn, and one of
them is green.You pick the red piece of candy from the rst urn and the green piece of candy from the
second. (Probability 1/2 *1/4 = 1/8 :) There is only one more piece of candy in the rst urn,
so you eat it on the second round.
You pick a red piece of candy from each urn. (Probability 1/2 *3/4 = 3/8 .)
Your chance of eating two pieces of green candy is
1/8
+
3/8
1/3
+
1/8
=
3/8
correct answer C
Answer: (C) 3/8
Question: An athlete runs 200 meters in 24 seconds. His speed is ?
(A) 10 km/hr
(B) 17 k/hr
(C) 27 km/hr
(D) 30 km/hr
(E) None of these
Rationale: ExplanaƟon:
Speed=DistanceTime=20024m/sec=253m/sec253
∗
185km/hr=30km/hr
Answer: D
Answer: (D) 30 km/hr
Question: In an election between the two candidates ,The candidates who gets 60% of votes polled is wined by 280 votes majority. What is the total number of votes polled?
(A) 1400
(B) 1500
(C) 1550
(D) 1600
(E) 1650
Rationale: Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %)
20 % = 60 % - 40 %
20% -----> 280 (20×14 = 280 )
100% -----> 1400 (100×14 = 1400)
A
Answer: (A) 1400
Question: Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers?
(A) 28
(B) 56
(C) 76
(D) 84
(E) 85
Rationale: Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 48
=> 12x = 48
=> x = 48/12 = 4
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 4 = 28
Answer: Option A
Answer: (A) 28
Question: How many options are there for a code consisting of 2 even digits followed by 2 odd digits?
(A) 4^5
(B) 5^4
(C) 5^5
(D) 4^4
(E) 10^4
Rationale: Even Numbers = 5 digits { 0 , 2 , 4 , 6 , 8 }
Odd Numbers = 5 digits { 1 , 3 , 5 , 7 , 9 }
EVEN EVEN ODD ODD
No of ways is 5*5*5*5 = 5^4
Hence, correct, answer must be (B) 5^4
Answer: (B) 5^4
Question: Evaluate the expression
[x : (y - 3)] ⋅ (-4) - [xy + (-3)] : -1 = ?
when x = -5 and y = -2
(A) 3
(B) 4
(C) 5
(D) 6
(E) None
Rationale: Solution:
Evaluate the expression
[x : (y - 3)] ⋅ (-4) - [xy + (-3)] : -1 =
[(-5) : (-2 - 3)] ⋅ (-4) - [(-5) ⋅ (-2) + (-3)] : -1 =
[(-5) : (-5)] ⋅ (-4) - [10 + (-3)] : -1 =
(+1) ⋅ (-4) - (+7) : -1 = -4 - (-7) = -4 + 7 = 3
Answer A
Answer: (A) 3
Question: If the given two numbers are respectively 7% and 28% of a third number, then what percentage is the first of the second ?
(A) 20%
(B) 25%
(C) 18%
(D) 30%
(E) none of these
Rationale: Here, l = 7 and m = 28
Therefore, first number = l/m x 100% of second number = 7/28 x 100% of second number = 25% of second number
ANSWER:B
Answer: (B) 25%
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 11 sec
(B) 15 sec
(C) 19 sec
(D) 12 seconds
(E) 20 sec
Rationale: D
D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: (D) 12 seconds
Question: If y = 35p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?
(A) p
(B) 2p
(C) 5p
(D) 7p
(E) p^2
Rationale: y = 35p = 5*7*p
14p = 2*7*p
The greatest common factor of 35p and 14p is the product of all the common prime factors, using the lower power of repeated factors. The greatest common factor is 7*p = 7p
The answer is D.
Answer: (D) 7p
Question: A man can do a piece of work in 6days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone?
(A) 5
(B) 5 1/2
(C) 7 1/2
(D) 6
(E) 9 1/2
Rationale: Son's 1day work = 1/3 - 1/6 = 1/6
Son alone can do the work in 6 days = 6 days
Answer is D
Answer: (D) 6