mathewhe/aqua_rat huggingface dataset:
Question: There are 11 software engineers and 7 civil engineers in a company. Theyare selecting member for row. In how many ways can they be seated in a row so that no two of the civil engineers will sit together?
(A) 10!×11!/5!
(B) 9!×11!/4!
(C) 11!×12!/5! ways
(D) 9!×5!/4!
(E) 5!×6!/7!
Rationale: 11 software engineers can be arranged in 11! ways. ...(A)
Now we need to arrange civil engineers such that no two civil engineers can be seated together. i.e., we can arrange 7 civil engineers in any of the 12 (=11+1) positions marked as * below.
* 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 *
(where 1, 2… 11 represent software engineers)
This can be done in 12P7 ways. ... (B)
From (A) and (B),
required number of ways
= 11! × 12P7
=11!×12!/5!
C
Answer: (C) 11!×12!/5! ways
Question: A train 1100 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 288 m
(B) 256 m
(C) 200 m
(D) 278 m
(E) 287 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (1100 + x)/60
= 65/3
x = 200 m.
Answer:C
Answer: (C) 200 m
Question: A man had 38 sheep. he wanted to divide them equally among his 6 children. How many sheep shall he keep to himself, so as to equally divide remaining sheep among his 6 children?
(A) 6
(B) 5
(C) 4
(D) 2
(E) 8
Rationale: Since he has 38 sheep and 6 children. The nearest number divisible by 6 is 36. So he would keep 2 sheep for himself and give 6 sheep to each child. So option D is correct.
Answer: (D) 2
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
(A) 624
(B) 702
(C) 756
(D) 812
(E) 832
Rationale: Total men are 7
Total women are 6 so we select 5 peoples in both and at least 3 are men
7c3*6c2+7c4*6c1+7c5*6c0 then we get the 756
ANSWER:C
Answer: (C) 756
Question: How many keystrokes are needed to type numbers from 1 to 1000?
(A) 2704
(B) 2890
(C) 2893
(D) 3001
(E) None of these
Rationale: 1-9
9 digits
10-99
There are 90 2-digit numbers
(90)(2) = 180 digits
100-999
There are 900 3-digit numbers
(900)(3) = 2700 digits
1000
4 digits
9 + 180 + 2700 + 4 = 2893
Answer: C
Answer: (C) 2893
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by seven when k is any of the following values EXCEPT
(A) -4
(B) -2
(C) -1
(D) 2
(E) 5
Rationale: We have the product of 3 integers: (x-1)x(x-k).
Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 7. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 7 these numbers must have different remainders upon division by 7, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 7.
Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 7. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 7.
Answer: E.
Answer: (E) 5
Question: The ratio, by weight, of coffee to mate to water in a certain cup of coffee is 6:2:15. The coffee is altered so that the ratio of coffee to mate is halved while the ratio of coffee to water is doubled. If the altered coffee will contain 16 grams of mate, how many grams of water does it contain after alteration?
(A) 12
(B) 15
(C) 30
(D) 60
(E) 100
Rationale: c:m:w = 6:2:15
new c:m = 1/2(6/2) = 3:2
new c:w = 2(6:15) = 12:15 = 4:5
so new m:c:w = 2:3
4:5
= 8:12:15 ( notice how i combined the two ratios by multiplication by 3 and 4 of respective ratios)
m = 16 g
Let T = total amount of c + m + w then
8 / (8+12+15)T = 16 x 35/8 = 70g
then w = 15/35 x 70 = 30g
Answer C
Answer: (C) 30
Question: A 210 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 290
(B) 280
(C) 270
(D) 260
(E) 250
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 210)/9 = 500/9 => x = 290.
Answer: Option A
Answer: (A) 290
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 10 multiples of 14, how many multiples of 7 are there in Q?
(A) 20
(B) 19
(C) 18
(D) 17
(E) 16
Rationale: Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 10+9 = 19.
The answer is B.
Answer: (B) 19
Question: The price of stock decreased by 8% last year and rose by 10% this year. What is the net percentage change in the price of the stock?
(A) 0.2%
(B) 0.8%
(C) 1.2%
(D) 1.6%
(E) 2%
Rationale: (100% - 8%) * (100% + 10%) = 0.92 * 1.10 =1.012 = 101.2%.
The net percentage change in the price of the stock is (+) 1.2%
The answer is C
Answer: (C) 1.2%
Question: A train is 360 meter long is running at a speed of 50 km/hour. In what time will it pass a bridge of 140 meter length.
(A) 26 seconds
(B) 36 seconds
(C) 46 seconds
(D) 56 seconds
(E) None of these
Rationale: Explanation:
Speed = 50 Km/hr = 50*(5/18) m/sec
= 125/9 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500/125/9 = 36 seconds
Answer: B
Answer: (B) 36 seconds
Question: Some people went for vacation. unfortunately it rained for 13 days when they were there. But whenever it rained in the morning, they had clean afternoon and vice versa. In all they enjoyed 11 morning and 12 afternoons. How many days did they stay there totally
(A) 16 days
(B) 17 days
(C) 18 days
(D) 19 days
(E) 15 days
Rationale: Whenever it rains, it only rains half a day.... so look at this problem in half days.The family was rained on for 13 {half days}, but they also had 11 + 12 {half days} of sun.So, 13 + 11 + 12 = 36 half days = 18 days
ANSWER:C
Answer: (C) 18 days
Question: 400 students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?
(A) 50
(B) 100
(C) 120
(D) 140
(E) 180
Rationale: 60%*x+80%*(400-x)=65%*400
Ans=100
ANSWER:B
Answer: (B) 100
Question: List I: 3, 6, 8, 11
List II: x, 3, 6, 8, 11
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: C.
Answer: (C) 7
Question: Solve the quickfire maths brain teaser âˆš16% = ?
(A) 30%
(B) 40%
(C) 85%
(D) 19%
(E) 29%
Rationale: âˆš16%
=> âˆš16/âˆš100
=> 4/10
=> 40/100
=> 40%
B
Answer: (B) 40%
Question: In how many ways letters of the word LEADER be arranged?
(A) 5
(B) 78
(C) 69
(D) 58
(E) 120
Rationale: LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways
E
Answer: (E) 120
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/8
II. 1/10
III. 1/11
(A) None
(B) I only
(C) III only
(D) II and III only
(E) II only
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us E as the only possible answer.
Answer: (E) II only
Question: If x = y+3+4.5x and y = x+24, what is the value of x/y ?
(A) -6/5.
(B) -7/20.
(C) -1/2.
(D) 5/6.
(E) 1.5.
Rationale: (1) x = y + 3 + 4.5x
Substitute y for y = x + 24 (Eq. we are given)
x = x + 24 + 3 + 4.5x
Combine like terms
x = 5.5x + 27 --> -4.5x = 27--> x = -6
(2) y = x + 18
Substitute x for x = -6
y = (-6) + 18 = 12
(3) x/y = ?
Substitute x and y we found above
x/y = (-6) / (12) = -1/2
My answer: C
Answer: (C) -1/2.
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) Rs. 9000
(B) Rs. 9800
(C) Rs. 9900
(D) Rs. 9990
(E) Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: (E) Rs. 10000
Question: If a2 - b2 = 5 and a*b = 2, find a4 + b4.
(A) 50
(B) 72
(C) 25
(D) 92
(E) 33
Rationale: a2 - b2 = 5 : given
a4 + b4 - 2a2b2 = 52 : square both sides and expand.
a*b = 2 : given
a2b2 = 22 : square both sides.
a4 + b4 - 2(4) = 25 : substitute
a4 + b4 = 33
correct answer E
Answer: (E) 33
Question: 8 red card number 1-8 put in one box， 8 blue card number 1-8，put in another box, take one card from each of the box，what is the probability that the number match each other?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 1/64
Rationale: Probability to pick a number from the first box - any of the 8 = 1..
prob to pick the same number from the 2nd box = 1/8..
Prob = 1∗1/8=1/8
Answer:C
Answer: (C) 1/8
Question: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days M will the work get over?
(A) 60
(B) 70
(C) M=75
(D) 80
(E) 100
Rationale: We can also use the concept of man-days here
100 days -->10men so the job includes 100*10=1000 man-days
After 20 days
1/4 of Job is completed so 1/4 X 1000 man-days=250 man-days Job is done
Now the Balance Job=1000-250=750 man-days worth of Job
Since 2 men are fired so B/L men=8
Therefore Total no. of days of Job=750 man-day/8 days = 375/4=94 days (approx.)
Now since this is total and Ques. is asking for additional no. of days,
So 94-20=74 days
The nearest approx. to answer is 75
Ans: C (75 days)
Answer: (C) M=75
Question: A and B can finish a work in 16 days while A alone can do the same work in 20 days. In how many days B alone will complete the work?
(A) 76 days
(B) 48 days
(C) 80 days
(D) 31 days
(E) 22 days
Rationale: B = 1/16 – 1/20 = 1/80 => 80 days
Answer: C
Answer: (C) 80 days
Question: List L: ABC, BCA, CAB
In list L above, there are 6 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
(A) 47
(B) 114
(C) 152
(D) 161
(E) 488
Rationale: Let's try to sum the 3 given numbers taking their place values into account:
(100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)
= 100(A + B + C) + 10(A + B + C) + (A + B + C)
= 111*(A + B + C)
We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152
Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.
Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3
A, B and C are all even. 2+4+8 = 14. Factors 2 and 7
Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.
E
Answer: (E) 488
Question: Robert's salary was decreased by 60% and subsequently increased by 60%. how much percentage does he lose?
(A) 10%
(B) 20%
(C) 25%
(D) 36%
(E) 50%
Rationale: let original salary be $100
Salary after decreasing 60% = 100 - 100 x 60/100 = $40
Salary after increasing 60% on $40 = 40 + 40 x 60/100 = $64
Percentage of loss = 100 - 64 = 36%
Answer : D
Answer: (D) 36%
Question: If 2x = 3y = 10, then 6xy = ?
(A)  100
(B)  200
(C)  120
(D)  40
(E)  20
Rationale: 2x = 10;x=5
3y = 10;y=10/3
Multiply: 6xy=6*5*10/3=100
Answer: A.
Answer: (A)  100
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 380$
(C) 525$
(D) 456$
(E) 480$
Rationale: Total Cost = ( 1.75*14 ) + ( 0.65 * 14* 55 ) = 24.5 + 500.5 => 525
Hence answer will be (C) 525
Answer: (C) 525$
Question: An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: Amount 1000 is invested for 12 yrs and yields 4000. Amount is compounded annually.
we need number of years it will take to yield 8000.
from 1000 to 4000 = 4 times
from 4000 to 8000 = 2 times.
if compounding is happening at same rate throughout, then
since, time required for 4 times = 12 yrs
=>time required for 2 times = 6 yrs
Total time from initial = 12+6 = 18 yrs
Ans B.
Answer: (B) 18
Question: When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $111.30, what was the total value of the item?
(A) $2380
(B) $2590
(C) $2760
(D) $2940
(E) $3150
Rationale: Let x be the value of the item.
0.07*(x-1000) = 111.30
x = 2590
The answer is B.
Answer: (B) $2590
Question: If x, y, and z are consecutive positive odd integers, not necessarily in that order, which of the following must be true? I. xy> z^4 II. (x + z)^3 > y III. x+y>z^4
(A) I only
(B) II only
(C) III only
(D) I,II only
(E) I,III only
Rationale: Lets suppose that a,b,c can take any one of following three value 1,5,7. Most important point is that the options MUST BE TRUE under any condition.
x+y>z^4
Not necessarily true as 1+5<2401
xz>y^4
Not necessarily true as 1.7<625
We don't need to check option as all the options except B can be discarded.
Thus Answer B
Answer: (B) II only
Question: Four of the five parts numbered as (a), (b), (c), (d) and (e)in the following equations are exactly equal. You have to find out the part that is not equal to the other parts. The number of that part is the answer.
(A) a2 + 5ab + 6b2
(B) (a + 3b)(a + 2b)
(C) a(a + 3b) + 2b(a + 3b)
(D) (3a + b)(a + 2b)
(E) a(a + 2b) + 3b(a + 2b)
Rationale: The other parts are equal to a2 + 5ab + 6b2.
Answer D
Answer: (D) (3a + b)(a + 2b)
Question: A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $55,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?
(A)  $27,500
(B)  $35,000
(C)  $37,500
(D)  $42,500
(E)  $50,000
Rationale: let x be the average of 40 customers
40*x + 10* 55000 = 50*45000
solving this we have x= 42500
Answer is D.
Answer: (D)  $42,500
Question: ravi decides to walk from goregaon to andheri .he has reached his destination in 2 hr 15 min by 4 of the distance at 6 kmph and the rest at 8 mph . how far goregaon from andheri?
(A) 11.6 km
(B) 12.6 km
(C) 13.6 km
(D) 14.6 km
(E) 15.6 km
Rationale: covering 3/t1+t2=9/4 hr
(3x/4*6)+(x/4*8*1.609)=9/4
x=15.6 km
ANSWER:E
Answer: (E) 15.6 km
Question: What is the value of 3x^2 − 1.8x + 0.6 for x = 0.6?
(A) −0.3
(B) 0.6
(C) 0.3
(D) 1.08
(E) 2.46
Rationale: 3x^2-1.8x+0.6 for x=0.6
=3(0.6*0.6)-3*0.6*(0.6)+0.6
=0+0.6
=0.6
ANSWER:B
Answer: (B) 0.6
Question: A person can row 750 metres against the stream in 11 ¼ minutes and returns in 7 ½ minutes. Then the speed of the person in in still water is :
(A) 2 km/hr
(B) 3 km/hr
(C) 4 km/hr
(D) 5 km/hr
(E) 6 km/hr
Rationale: The speed in upstream = .75 * (4/45 )*60 = 4 kmph
The speed in downstream = .75 *(2/15) *60 = 6 kmph
Speed in still water = ½(4+6) = 5 kmph
ANSWER:D
Answer: (D) 5 km/hr
Question: A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income?
(A) Rs.900
(B) Rs.800
(C) Rs.500
(D) Rs.1000
(E) Rs.1200
Rationale: X * 4/5 * 80/100 = 576
X = 14400/16
X = 900
ANSWER:A
Answer: (A) Rs.900
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
5 * 7 * 9 = 68
Then find,
7 * 9 * 11 =?
(A) 106
(B) 49
(C) 68
(D) 38
(E) 55
Rationale: A
106
(11 * 9) + 7 = 106
Answer: (A) 106
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 2. The numbers are
(A) 12, 24, 30
(B) 12, 24, 38
(C) 12, 24, 362
(D) 2, 4, 6
(E) 12, 24, 321
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 2
\inline \fn_jvn \therefore The numbers are 2, 4, 6
Answer: D) 2, 4, 6
Answer: (D) 2, 4, 6
Question: Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
(A) 10.5
(B) 15
(C) 15.5
(D) 30
(E) 60
Rationale: The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 10
x=15.5 minutes
Answer: C
Answer: (C) 15.5
Question: In a flower shop there were 7 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
(A) 12
(B) 11
(C) 14
(D) 9
(E) None of these
Rationale: Answer
Now required average
= old average x Multiplicand
= 7 x 2 = 14
Correct Option: C
Answer: (C) 14
Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
(A) 30%
(B) 33 1/3%
(C) 37 1/2%
(D) 40%
(E) 50%
Rationale: Initial solution => 8 kg (x:w :: 2.4:5.6)
After evaporation Initial solution => 6 kg (x:w:: 2.4:3.6)
New solution => 2 kg (x:w::0.6:1.4)
Mixing (Initial solution + New solution) => 6 kg (2.4:3.6)+ 2 kg (0.6:1.4) =
= 8 kg [(2.4+0.6) : (3.6+1.4)]
= 8 kg (x : water :: 3kg : 5 kg)
Hence % of x = 3/8 = 37.5%
ANSWER:C
Answer: (C) 37 1/2%
Question: A man can do a piece of work in 7 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone?
(A) 5
(B) 7
(C) 15/2
(D) 21/4
(E) 18/5
Rationale: Son's 1 day's work = (1/3)-(1/7) = 4/21
The son alone can do the work in 21/4 days
Answer is D
Answer: (D) 21/4
Question: The number of new words that can be formed by rearranging the letters of the word 'NOTE' is ?
(A) 118
(B) 290
(C) 23
(D) 120
(E) 140
Rationale: Number of words which can be formed
= 4! - 1 = 24 - 1
= 23.
Answer:C
Answer: (C) 23
Question: Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Rs 15
(B) Rs 12.10
(C) Rs 21.70
(D) Rs 16.80
(E) None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 27 - 5 - 0.30
=21.70
Answer : C
Answer: (C) Rs 21.70
Question: Manu, Manju and Maya can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete work?
(A) 15
(B) 10
(C) 20
(D) 25
(E) 30
Rationale: Manu’s one day’s work = 1/90
Manju’s one day’s work = 1/30
Maya’s one day’s work = 1/45
Manu, Manju and Maya together can do the work = 1/90 + 1/30 + 1/45
= (1+3+2)/90
= 1/15
So, They will complete the work in 15 days.
ANSWER:A
Answer: (A) 15
Question: X can do a piece of work in 20days. He works at it for 10days and then Y finished it in 12days. How long will Y take to complete the work?
(A) 10
(B) 12
(C) 24
(D) 29
(E) 30
Rationale: Work done by X in 10days = 10*1/20 = 1/2
Remaining work = 1 - 1/2 = 1/2
1/2 work is done by Y in 12days
Whole work will be done by Y in 12*2 = 24days
Answer is C
Answer: (C) 24
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
(A) 2277
(B) 8000
(C) 2688
(D) 1266
(E) 1912
Rationale: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer: B
Answer: (B) 8000
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
(A) 377
(B) 267
(C) 268
(D) 750
(E) 271
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 .Answer: D
Answer: (D) 750
Question: What is the smallest integer k for which 64^k > 4^22?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 64^k > 4^22
4^(3k) > 4^22
3k > 22
k = 8
The answer is E.
Answer: (E) 8
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/7
(B) 9/6
(C) 5/9
(D) 5/6
(E) 3/6
Rationale: Explanation:
P(at least one graduate) = 1 - P(no graduates) =
1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6
Answer: Option D
Answer: (D) 5/6
Question: Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 22 kmph and Prasanna moves southward at a speed of 24 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
(A) 44
(B) 50
(C) 28
(D) 27
(E) 18
Rationale: Explanation:
We know 60 min = 1 hr
Total northward Laxmi's distance = 22kmph x 1hr = 22 km
Total southward Prasanna's distance = 24kmph x 1hr = 24 km
Total distance between Prasanna and Laxmi is = 22 + 24 = 44 km.
Answer: A
Answer: (A) 44
Question: GINGER has 3 pairs of pants, 4 different colored dress shirts 3 sports jackets, 9 ties, and 1 pairs of dress shoes in his closet. How many different outfits can he select?
(A) 324
(B) 312
(C) 290
(D) 115
(E) 352
Rationale: no. of ways he can select a pant = 3
no. of ways he can select a shirt= 4
number of ways he can select a pant = 3
number of ways he can select a shirt= 4
similarly, he can select jacket by 3 ways, tie by 9 ways and shoe by 1 way
number of ways to select different outfits = 3*4*3*9*1 =324
Answer:A
Answer: (A) 324
Question: In a lottery, there are 10 prizes and 30 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/10
(B) 2/5
(C) 2/7
(D) 1/4
(E) None
Rationale: Solution
P(getting a prize)	= 10 / (10+30)
‹=› 10 / 40
‹=› 1 / 4.
Answer D
Answer: (D) 1/4
Question: James takes a trip and drives 7 hours from Town A to Town C at a rate of 30 miles per hour. On his way back, James drives 60 miles per hour and stops in Town B which is midway between Town A and Town C. How many hours does it take James to drive from Town C to Town B?
(A) 1.25
(B) 1.75
(C) 1.51
(D) 1.55
(E) 2.12
Rationale: distance from A to C =7 hr* 30 mph= 210 miles
hence distance from Y to C= 1/2*210=105
time=105/60=1.75 hrs
IMO: B
Answer: (B) 1.75
Question: The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:
(A) 0.4
(B) 0.004
(C) 0.04
(D) 0.0004
(E) None of them
Rationale: Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x (x) = 2 x 11.98 x 0.02 or
x = 0.04
Answer is C.
Answer: (C) 0.04