divelab/Sys2Bench huggingface dataset:
Question: A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?
Options:
A)A-20.
B)A-12.
C)A-9.
D)A-10.
E)A-13.
Rationale: We could use the following logic:
since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n).
The condition here should now be
11K + 1 = <operation> such that it gives us an integer
11k +1 = A -20 => A = 11K + 21 Not divisible by 11
11K +1 = A -12 => A = 11K + 31 Not Divisible by 11
11K +1 = A -9 => A = 11K + 10 Not Divisible by 11
11K +1 = A -10 => A = 11K + 11Divisible by 11
11K +1 = A -13 => A = 11K + 14 Not Divisible by 11
Answer therefore is A -10 (D)
Answer: D
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
Options:
A)120
B)720
C)125
D)729
E)None of these
Rationale: Explanation :
The first ring can be worn in any of the 3 fingers
=> There are 3 ways of wearing the first ring
Similarly each of the remaining 5 rings also can be worn in 3 ways
Hence total number of ways
=3×3×3×3×3×6=36=729. Answer : Option D
Answer: D
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 17 kmph, 18 kmph, 19 kmph, and 20 kmph respectively. What is the ratio of the time taken by B to than taken by D?
Options:
A)5:16
B)5:17
C)9:8
D)10:9
E)None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D =20 : 18 = 10 : 9.
Answer : D
Answer: D
Question: A train of length 560 metres takes 90 seconds to cross a tunnel of length 340 metres. What is the speed of the train in km/hr?
Options:
A)36 km/hr.
B)46 km/hr.
C)30 km/hr.
D)48 km/hr.
E)None
Rationale: Sol.
Speed = [560+340 / 90] m/sec = [900 / 90 * 18/5] km/hr = 36km/hr.
Answer A
Answer: A
Question: In the coordinate plane, points (x, 5) and (9, y) are on line k. If line k passes through the origin and has slope 5/9, then x - y =
Options:
A)4
B)6
C)5
D)8
E)7
Rationale: Line k passes through the origin and has slope 1/4 means that its equation is y=5/9*x.
Thus: (x, 5)=(9, 5) and (9, y) = (9,5) --> x-y=9-5=4.
Answer: A
Answer: A
Question: A bus can hold 120 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?
Options:
A)10
B)12
C)45
D)8
E)9
Rationale: No. of seats = 120/12 = 10
There are 10 seats in each row
Answer : A
Answer: A
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Options:
A)2400
B)2408
C)2406
D)2403
E)2401
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: A
Question: A typist can type 120 words in 100 seconds. At that rate, how many seconds would it take her to type 258 words?
Options:
A)205
B)210
C)215
D)220
E)225
Rationale: 120/100=258/n
120* n=258*100
120n	=25800
n=215
Answer:C
Answer: C
Question: A bag contains 12 red jellybeans and 12 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability that all 3 jellybeans removed from the bag are blue?
Options:
A)9/100
B)2/19
C)1/8
D)3/20
E)3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability = 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 3/10
Answer: option E
Answer: E
Question: If A lends Rs.3150 to B at 8% per annum and B lends the same sum to C at 12.5% per annum then the gain of B in a period of 2 years is?
Options:
A)280
B)295
C)283.5
D)245
E)200
Rationale: (3150*4.5*2)/100
=> 283.5
Answer: C
Answer: C
Question: In how many ways can the digit of the number 2233558888 be arranged so that the odd digits are placed in the even positions?
Options:
A)380
B)400
C)430
D)450
E)480
Rationale: odd place combination = 5!/2!*2!=30
even place combination= 6!/2!*4!=15
to total=30*15=450
ANSWER:D
Answer: D
Question: A solution of X pounds of water and sugar is boiled until 20% of the water content evaporates. Originally s% of sugar was present in the solution. After evaporation, what percentage of the solution is sugar?
Options:
A)100s/(1-s)
B)80s/(1-s)
C)75s/(1-s)
D)100s/(80-0.2s)
E)100s/(80+0.2s)
Rationale: We'll go for the ALTERNATIVE approach since there are variables in all the answers (which means that any number could work). Since the question deals with percents, the easiest number to use is X = 100. Now let's say that s = 10. Before the evaporation we had 10 pound of sugar and 90 pounds of water. Since only water evaporated, after the evaporation the 10 pounds of sugar remained the same, but the water reduced by 20% of 90 (18 pounds), so we have only 72 pounds of water. 10 out of 82 is the fraction of sugar, so if we multiply it by 100 we get the percents. The correct answer is E: 100s/(80+0.2s) >>> 100x10 / 82
Answer: E
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
Options:
A)10.5%
B)12.5%
C)15%
D)22%
E)30%
Rationale: Say there are 100 motorists.
{# of motorists who exceed speed & receive tickets} + {# of motorists who exceed speed & don't receive tickets} = {Total # of motorist who exceed speed};
Given: {# of motorists who exceed speed & receive tickets}=10;
Also, if {Total # of motorist who exceed speed}=x, then 0.2x={# of motorists who exceed speed & don't receive tickets};
10+0.2x=x --> x=12.5
Answer: B.
Answer: B
Question: At the opening of a trading day at a certain stock exchange, the price per share of stock M was $25. If the price per share of stock M was $28 at the closing of the day, what was the percent increase in the price per share of stock M for that day?
Options:
A)1.4%
B)5.9%
C)12%
D)12.5%
E)23.6%
Rationale: Opening = 25
Closing = 28
Rise in price = 3
So, percent increase = 3/25*100 = 12
Answer : C
Answer: C
Question: From the integer n, if n*n*n*n is even, then what is true from below options?
Options:
A)n is odd
B)n*n is even
C)n is odd and n*n is even
D)n is even
E)None
Rationale: n is even
Option D
Answer: D
Question: What is the sum of the greatest common factor and the lowest common multiple of 16 and 36?
Options:
A)124
B)152
C)148
D)123
E)412
Rationale: Prime factorization of 16 = 2 x 2 x 2 x 2
Prime factorization of 36 = 2 x 2 x 3 x 3
GCF=4
LCM=144
Sum=148
Option: C
Answer: C
Question: John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 4 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
Options:
A) 4y
B) 5y
C) 6y
D) 8y
E) 9y
Rationale: Let $x be the advance that both receive = 4x
Amount earned per hour by John and Mary = x/10 and x/6
Mary gives $y to John to make the wages earned equal
Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/6
Solve (x+y)10 = (x-y)/6
6x + 6y = 10x -10y
4x = 16y
x = 4y
Ans. A
Answer: A
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
Options:
A)(0.6)^5
B)2(0.6)^4
C)3(0.6)^4
D)4(0.6)^4(0.4) + (0.6)^5
E)5(0.6)^4(0.4) + (0.6)^5
Rationale: P(h)=0.6P(h)=0.6, so P(t)=0.4P(t)=0.4. We want to determine the probability of at least 4 heads in 5 tries.
At least 4 heads means 4 or 5. Let's calculate each one:
5 heads: P(h=5)=0.6^5;
4h and 1t: P(h=4)=5!/4!∗0.6^4∗0.4=5∗0.6^4∗0.4, multiplying by 5 as 4h and 1t may occur in 5 different ways:
hhhht
hhhth
hhthh
hthhh
thhhh
So, P(h≥4)=0.6^5+5∗0.6^4∗0.4
Answer: E.
Answer: E
Question: Three numbers are in the ratio 5 : 4 : 3 and their average is 360. The largest number is :
Options:
A)30
B)450
C)27
D)21
E)22
Rationale: Explanation:
Let the numbers be 5x, 4x and 3x, Then, (5x + 4x + 3x ) / 3 =360
=> 12x = 360*3
=> x = 90
Largest number 5x = 5*90 = 450
Answer: B
Answer: B
Question: A radio station has to choose 6 days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any 6 of the seven weekdays can be chosen. How many different 6-day combinations of the seven weekdays can be constructed?
Options:
A)7
B)15
C)21
D)35
E)56
Rationale: Pick 6 days out of 7.. 7C6 = 7
Answer : A
Answer: A
Question: The positive numbers w, x, y, and z are such that x is 20 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?
Options:
A)15.2%
B)16.0%
C)20.0%
D)23.2%
E)24.8%
Rationale: y = 100 (start with yy, it makes getting x easier).
x = y*1.2 = 120
z = y/1.2 = 83.33
w = x*0.8 = 96
Then for the answer:
(w-z)/z = (96 - 83.33)/83.33
= 15.2%
ANSWER:A
Answer: A
Question: A seller sells his apple at CP but uses a weight of 800 gm instead of kg weight. What is his profit %?
Options:
A)20%
B)23%
C)25%
D)30%
E)32%
Rationale: If a trader professes to sell his goods at cost price, but uses false weights, then
Gain%=[Error(True Value−Error)×100]%So here profit percentage=[200(1000−200)×100]%=[200800×100]%=25%
C
Answer: C
Question: Today is Thursday. The day after 59 days will be?
Options:
A)Monday
B)Tuesday
C)Saturday
D)Sunday
E)wednesday
Rationale: Explanation:
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Thursday, After 59 days, it will be = (Thursday + 3 odd days)
= Sunday
Answer: Option D
Answer: D
Question: M and B are integers. The expression (M+1)(B+1) is even. What can be said about M and B?
Options:
A)They are both even numbers.
B)At least one of them is even.
C)At least one of them is odd.
D)They are both odd.
E)Nothing can be said surly on M and B
Rationale: Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (M+1) or (B+1) needs to be Even
So either M or B needs to be odd
Or At least one of them is odd.
At least one of them is odd=C
Answer: C
Question: A shirt goes on sale for 80% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?
Options:
A)72%
B)70%
C)52%
D)50%
E)28%
Rationale: Just assume original price is 100.
Sale price = 80
Then it is marked down by 10% = 80-8=72.
Hence it is 72% of the original price. Hence answer is A
Answer: A
Question: Sakshi can do a piece of work in 12 days. Tanya is 20% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: Ratio of times taken by Sakshi and Tanys = 120:100 = 6:5
Suppose Tanya takes x days to do the work.
6:5 :: 12:x => x= 10 days.
Hence, Tanya takes 10 days to complete the work.
Answer: A
Answer: A
Question: The LCM and HCF of two numbers are 100000 and 10000 respectively. Find the larger of the two numbers if their sum is 110000.
Options:
A)100000
B)46
C)577
D)577
E)767
Rationale: There are 2 approaches in solving this.
Methode 1.
HCF * LCM = The Actual Number.
100000* 10000= 1000000000
So the answer which we are looking for has to be a factor of 1000000000.
So among the options shortlist the answers by eliminating those numbers which is not divisible by 1000000000. and then take the highest number as the answer as the question asks abt the highest number.
answer is A
Answer: A
Question: How many words can be formed by using all letters of the word ‘PENCIL’ ?
Options:
A)480
B)600
C)720
D)900
E)1060
Rationale: The word contains 6 different letters.
The number of permutations is 6! = 720
The answer is C.
Answer: C
Question: if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (648)5
Options:
A)14.05
B)14.02
C)277
D)288
E)222
Rationale: log(648)5
= 5 log(648)
= 5 log(81 × 8)
= 5[log(81) + log(8)]
=5 [log(34) + log(23)]
=5[4log(3) + 3log(2)]
= 5[4 × 0.4771 + 3 × 0.30103]
= 5(1.9084 + 0.90309)
= 5 × 2.81149
≈ 14.05
Answer: A
Answer: A
Question: In an university college, the ratio of the number of boys and girls is 5 : 9. If the percentage increase in the number of boys and girls be 20% and 40% respectively. What will be the new ratio ?
Options:
A)21 : 10
B)12 : 17
C)15 : 23
D)10 : 21
E)None of these
Rationale: Explanation :
Solution: Originally, let the number of boys and girls in the university college be 5x and 9x respectively.
Their increased number is (20% of 5x) : (40% of 9x)
=> (120*5x/100) : (140*9x/100) = 60x : 126x
=> x : y = 10 : 21.
Answer : D
Answer: D
Question: John was thrice as old as Tom 6 years ago. John will be 3/2 times as old as Tom in 6 years. How old is Tom today?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: J-6 = 3(T-6), so J = 3T-12
J+6 = 3/2 * (T+6)
2J + 12 = 3T + 18
2(3T-12) + 12 = 3T + 18
3T = 30
T = 10
The answer is C.
Answer: C
Question: A sum of money amounts to Rs 9800 after 5 years and Rs 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
Options:
A)9%
B)10%
C)11%
D)12%
E)13%
Rationale: Explanation:
We can get SI of 3 years = 12005 - 9800 = 2205
SI for 5 years = (2205/3)*5 = 3675 [so that we can get principal amount after deducting SI]
Principal = 12005 - 3675 = 6125
So Rate = (100*3675)/(6125*5) = 12%
Option D
Answer: D
Question: The sum of the first 30 positive even integers is 930. What is the sum of the first 30 odd integers?
Options:
A)930
B)900
C)960
D)975
E)980
Rationale: Sum of first n even numbers = n(n+1) =930
Sum of first n odd numbers = n^2 = 30*30 = 900 (here n=30)
Answer : B
Answer: B
Question: If a(a + 7) = 60 and b(b + 7) = 60, where a ≠ b, then a + b =
Options:
A) −7
B) −2
C) 2
D) 46
E) 48
Rationale: i.e. if a = 5 then b = -12
or if a = -12 then b = 5
But in each case a+b = -12+5 = -7
Answer: option A
Answer: A
Question: There is a 50% chance Jen will visit Chile this year, while there is a 50% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?
Options:
A)25.0%
B)50.0%
C)62.5%
D)75.0%
E)80.0%
Rationale: P(Chile and not Madagascar) = 0.5*0.5 = 0.25
P(Madagascar and not Chile) = 0.5*0.5 = 0.25
Total probability = 0.25 + 0.25 = 0.5 = 50%
The answer is B.
Answer: B
Question: Find the remainder when the polynomial x4 - 3x2 + 7x - 10 is divided by (x - 2).
Options:
A)8
B)-20
C)18
D)0
E)None
Rationale: Explanatory Answer
By remainder theorem: If a polynomial in one variable 'x' is divided by (x - a), where 'a' is any real number, then the remainder is the value of the polynomial at x = a.
Therefore, remainder = (2)4 - 3(2)2 + 7(2) - 10 = 8
Answer A
Answer: A
Question: Robert invests $120,000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Jody invests $120,000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Robert's account, approximately how much more does Jody’s account have?
Options:
A)Zero
B)$81.90
C)$819.00
D)$8190.03
E)$81900.30
Rationale: Robert's interest= $120,000*0.12 = $14400 or $1,200 each month.
Jody’s interest, 12%/12 = 1% each month:
For the 1st month = $120,000*0.01 = $1,200;
For the 2nd month = $1,200 + 1% of 1,200 = $1,212, so we would have interest earned on interest (very small amount);
For the 3rd month = $1,212 + 1% of 1,212 = ~$1,224;
For the 4th month = $1,224 + 1% of 1,224 = ~$1,236;
...
For the 12th month = $1,320 + 1% of 1,320 = ~$1,332.
The difference between Robert's interest and Jody's interest = ~(12 + 24 + ... + 132) = $792.
Answer: C.
Answer: C
Question: What two-digit number is less than the sum of the square of its digits by 15 and exceeds their doubled product by 5?
Options:
A) 95
B) 99
C) 26
D) 73
E) None of the Above
Rationale: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -15
Thus 2xy +5 = x^2 + y^2 - 15
x^2 + y^2 -2xy = 16
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 73
Thus the answer is D
Answer: D
Question: The wages of 24 men and 16 women amount to 11600 per day. Half the number of men and 37 women has same money. The daily wages paid to each man is
Options:
A)223
B)350
C)31887
D)2797
E)911
Rationale: 24m + 16w = 11600
12m + 37 w = 11600
Solving we get 12 m = 21w
Substituting in the first equation we get, 42w + 16 w = 11600 ⇒⇒ w = 200
M = 350
Answer:B
Answer: B
Question: If x/4 years ago Roger was 14 years old and x/4 years from now he will be 4x years old, how old will he be 3x years from now?
Options:
A)32
B)35
C)30
D)40
E)27
Rationale: Assume the current age = a
a - x/4 = 14 (i)
a + x/4 = 4x
Or a = 15x/4 (ii)
Putting the value of a from (ii) in (i)
15x/4 - x/4 = 14
Or 14x/4 = 14 Therefore x = 4 and a = 15
3x years from now, age will be 15 + 3*4 = 27
Option E
Answer: E
Question: 1397 x 1397 = ?
Options:
A)1951000
B)1951500
C)1951509
D)1951511
E)1951609
Rationale: 1397 x 1397	= (1397)^2
= (1400 - 3)^2
= (1400)2 + (3)2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
E)
Answer: E
Question: If n is an integer from 1 to 96 (inclusive), what is the probability for n*(n+1)*(n+2) being divisible by 8?
Options:
A)25%
B)50%
C)62.5%
D)72.5%
E)75%
Rationale: (A) 25% , to be divisible by 8 the number needs to have 3 2s in it. Only a multiple of 4 can provide that. Number of numbers divisible by 4 = 96/4 = 24. So P(8) = 24/96 = 25% .
Answer: A
Question: 36 workers can reap a field in 6 days. If the work is to be completed in 4 days, the extra workers required are
Options:
A)10
B)25
C)18
D)15
E)16
Rationale: Explanation:
M1D1 = M2D2
36(6)=X(4)
=54
Extra required workers are 54-36=18
Answer: Option C
Answer: C
Question: Ten years ago, P was half of Q's age. If the ratio of their present ages is3:4, what will be the total of their present ages?
Options:
A)45
B)40
C)35
D)30
E)25
Rationale: Let present age of P and Q be
3x and
4x respectively.
Ten years ago, P was half of Q's age
⇒(3x−10)=1(4x−10)/2
⇒6x−20=4x−10
⇒2x=10
⇒x=5
Total of their present ages
3x+4x=7x=7*5=35
ANSWER:C
Answer: C
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 60 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
Options:
A)160
B)240
C)330
D)440
E)560
Rationale: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 60.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*60 = 270.
Total area = 60 + 270 =330.
Answer: C.
Answer: C
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
Options:
A)32:21
B)22:21
C)21:32
D)31:21
E)32:28
Rationale: Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000*6 + 15000*6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000*4 : 50000*4)
Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)
= (20*6 + 15*6) : (30*4 + 50*4)
= (20*3 + 15*3) : (30*2 : 50*2)
= 105:160
= 21:32
Answer is C
Answer: C
Question: N* is defined as 0.5(N+10) for any number N. What is N, if ((N*)*)*=15?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: N*=0.5(N+10)
(N*)*=0.5(0.5N+5+10)= 0.25N+7.5
((N*)*)*=0.5(0.25N+7.5+10)= 0.125N+8.75
we know that ((N*)*)*=15
0.125N+8.75=15
0.125N=6.25
N= 6250/125= 50
ANSWER:D
Answer: D
Question: In an election between two candidates, 10% of votes are were declares invalid. First candidate got 1800 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was:
Options:
A)9000
B)9900
C)10000
D)11000
E)12000
Rationale: 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 1800 ( 18 × 100 = 1800)
100% -------> 10000 votes (100 × 100 = 10000)
C
Answer: C
Question: A man drive his car to the office at 20miles/hr.
After reaching office, he realize that its a new year holiday so he went back home at a speed of 30miles/hr.
Discounting the time spent in the stoppage what was his average speed of his journey ?
Options:
A)21
B)20
C)25
D)24
E)29
Rationale: D
24miles/hr (not 25miles/hr which might be guessed by many)
D : distance traveled
T1 : time of going to office
T2 : time of returning back
Y : Average Speed
D = 20 * T1
T1 = D/20
D = 30 * T2
T2 = D/30
2D = Y(T2 + T1)
2D = Y(D/20 + D/30)
2D = Y(3D/60 + 2D/60)
2D = Y(5D/60)
Y = 120D/5D
=> Y = 24
Answer: D
Question: Pat is now 22 years older than Dan. If in 6 years Pat will be twice as old as Dan, how old will Pat be in 15 years?
Options:
A)47
B)49
C)51
D)53
E)55
Rationale: P=D+22 so D=P-22.
P+6=2(D+6).
P+6=2(P-22+6).
P+6=2P-32.
P=38.
In 15 years, Pat will be 53 years old.
The answer is D.
Answer: D
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Options:
A)299
B)278
C)278
D)480
E)281
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
Answer: D
Answer: D
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur. What is the probability that event A occurs?
Options:
A)1/12
B)1/8
C)1/6
D)1/3
E)2/3
Rationale: Let us say probability of A occurring is a.
Let us say probability of B occurring is b.
a = 2b
Probability (either A or B or both) = 8 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 8*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 8*2b*b
3b-2b^2 = 16b^2
3b = 18b^2
b = 3/18 = 1/6
So, a = 2b = 1/3
ANSWER:D
Answer: D
Question: Calculate the average of first 14 even numbers is?
Options:
A)11
B)15
C)16
D)14
E)12
Rationale: Explanation:
Sum of 14 even numbers = 14 * 15 = 210
Average = 210/14 = 15
Answer: Option B
Answer: B
Question: A and B invests Rs.12000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.30000, find their shares?
Options:
A)s.12000, Rs.15020
B)s.12000, Rs.15700
C)s.12000, Rs.15090
D)s.12000, Rs.15000
E)s.12000, Rs.18000
Rationale: The ratio of their profits A:B
= 8:12 = 2:3
Share of A in the total profit
= 2/5 * 30000
= Rs.12000 Share of A in the total profit = 3/5 * 30000
= Rs.18000
Answer: E
Answer: E
Question: If 10^(z-1)< 0.000125 <10^z, what is the value of an integer z?
Options:
A)-4
B)-3
C)-2
D)3
E)4
Rationale: -> Multiply 10^6- > (10^6){10^(z-1)}<125<(10^6)(10^z) -> 125 is bigger than 100
-> (10^6)(10^(z-1))=100 -> 10^(6+z-1)=10^2, z+5=2 -> z=-3
Thus, the answer is B
Answer: B