divelab/Sys2Bench huggingface dataset:
Question: Excluding stoppages, the speed of a bus is 5454 kmph and including stoppages, it is 4545kmph. For how many minutes does the bus stop per hour?
Options:
A)12
B)11
C)10
D)9
E)8
Rationale: Explanation:
Speed of the bus excluding stoppages =54=54 kmph
Speed of the bus including stoppages =45=45 kmph
Loss in speed when including stoppages =54âˆ’45=9 kmph=54âˆ’45=9 kmph
â‡’â‡’ In 11 hour, bus covers 99 km less due to stoppages.
Hence, time in which the bus stops per hour
= Time taken to cover 99 km
=distancespeed=954 hour=16 hour =distancespeed=954 hour=16 hour =606 min=10 min
ANSWER IS C
Answer: C
Question: For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 4 is in the set , which of the following must also be in the set ?
a) 4
b) 1
c) -5
Options:
A)a only,
B)b only,
C)c only,
D)a and b only
E)b and c only
Rationale: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.
Since 1 is in the set, then so must be 4-3=1. Similarly, since 1 is in the set, then so must be 1-3=-2. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.
Answer: B.
Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: B
Question: 5^100 is divided by 18. Then what is the remainder?
Options:
A)11
B)14
C)13
D)16
E)17
Rationale: Here N = 18=2×32
ϕ(18)=18(1−12)(1−13) = 6
So 56 when divided by 18, remainder is 1.
So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49
Now 49 when divided by 18, remainder is 13.
C
Answer: C
Question: If two letters are chosen at random (without replacement) from the word EQUAL, what is the probability that none of the letters are vowels?
Options:
A)1/5
B)2/5
C)1/10
D)3/10
E)3/20
Rationale: The number of ways to choose two letters is 5C2 = 10
The number of ways to choose two consonants is 2C2 = 1.
P(no vowels) = 1/10
The answer is C.
Answer: C
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
Options:
A)3
B)4
C)5
D)8
E)10
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: D
Question: In how many ways can a five-letter password be chosen, using the letters A, B, C, D, E, F, G, and/or H such that at least one letter is repeated within the password?
Options:
A)720
B)864
C)900
D)936
E)26048
Rationale: Total number of four letter passwords = 8*8*8*8*8= 32768 ------(1)
Total number of passwords in which no letter repeats = 8C5*5!= 56*120=6720------(2)
therefore required value = (1)-(2)= 32768-6720=26048
E
Answer: E
Question: A car covers 4 successive 3km stretches at speed of 10kmph, 20kmph, 30kmph & 60kmph resp. Its average speed is
Options:
A)20 km/h
B)25 km/h
C)30 km/h
D)35 km/h
E)45 km/h
Rationale: Average speed = total distance / total time
total distance = 4 * 3 = 12 km
total time = 3/10 + 3/20 + 3/30 + 3/60
= 36/60 hr
speed =12/36 * 60 = 20 kmph
Answer : A.
Answer: A
Question: A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?
Options:
A)90
B)115
C)130
D)144
E)195
Rationale: Case 1 PPNN 2 Poems out of 4 and 2 Novels out of 6 i.e. 4C2 * 6C2 = 90
or
Case 2 PPPN 3 Poems out of 4 and 1 Novels out of 6 i.e 4C3 * 6C1 = 24
or
Case 3 PPPP 4 Poems out of 4 i.e. 4C4 =1
Total no. of selections case 1 + case 2+ case 3 = 90 + 24 +1 = 115
So answer must be B. 115
ANSWER:B
Answer: B
Question: The sum an integer N and its reciprocal is equal to 78/15. What is the value of N?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Write equation in N as follows
N + 1/N = 78/15
Multiply all terms by N, obtain a quadratic equation and solve to obtain N = 5.
correct answer C
Answer: C
Question: An accurate clock shows 5 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 11 o'clock in the morning?
Options:
A)140º
B)160º
C)180º
D)200º
E)210º
Rationale: Angle traced by the hour hand in 6=(360x12)x6º = 180º.
answer :C
Answer: C
Question: How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0, 1, 2, 3, 4, 5 (WITHOUT REPETITION)
Options:
A)216
B)3152
C)240
D)600
E)305
Rationale: Divisibility rule for 3: Sum of all digits is a multiple of 3
Selections for the above to be valid
1,2,3,4,5
No of possible ways = 5! = 120
0,1,2,4,5
No of possible ways = 4*4! = 96
Total = 120+96 = 216
ANS:A
Answer: A
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 3 muffins remained. How many guests did Monica plan on?
Options:
A)3.
B)4.
C)5.
D)6.
E)7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 3 = 5x + 2
6x - 3 = 5x + 2
x = 5
Answer: C
Answer: C
Question: Two pipes P and Q can fill a cistern in 10 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)1/2
B)1/4
C)2/4
D)1/4
E)1/4
Rationale: 3/10 + x/15
= 1
x= 10 1/2
Answer: A
Answer: A
Question: In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?
Options:
A)2 people
B)6
C)14
D)16
E)24
Rationale: FIRST OFFUnderstand what you are trying to find - In this case, you are trying to find how many people rank Vanilla first. For someone to rank Vanilla first, they have to rank them before Chocolate or Strawberry. This should be the very first hint that the correct answer cannot be bigger than 1/10 * 60 = 6.
So if you are time pressured on the real test, at least you narrowed down the selections to two choices - not bad. But what now?
Solve the easier problem. From 60 people, we are already told that 3/5 of them rank Vanilla last, leaving us with 2/5 of the people not ranking vanilla last - 24 people. So what are those combinations that vanilla are not last?
A) C, V, S
B) S, V, C
C) C, S, V (vanilla first)
D) S, C, V (vanilla first)
What are we ultimately hunting for here? The number of people that rank vanilla first:C+D
Now let's represent the given info into three equations
1) A+B+C+D = 24(2/5 of the people do not rank vanilla last)
2) A+C+D = 6(1/10 rank vanilla before chocolate)
3) B+C+D = 20(1/3 rank vanilla before strawberry)
Subtract equation 1 from 2, leaving us with
B = 24 - 6 = 18
Sub in B into equation 3 and solve for C+D
18 + C + D = 20
C+D = 20 - 18 = 2
There you go! 2 people out of the 60 ranked Vanilla as first A
Answer: A
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 135 grams of water?
Options:
A) 16
B) 72
C) 112
D) 120
E) 142
Rationale: Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water.
Therefore there are 135*8/9=120 grams of oxygen in 135 grams of water.
Answer: D.
Answer: D
Question: If (x/y)=(7/5), find the value (x^2+y^2)/(x^2-y^2)
Options:
A)37/12
B)59/11
C)51/77
D)41/11
E)None of them
Rationale: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(7/5)^2+1] / [(7/5)^2-1]
= [(49/25)+1] / [(49/25)-1] = 37/12
Answer is A.
Answer: A
Question: A man can row his boat with the stream at 20 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)7 kmph
C)98 kmph
D)6 kmph
E)8 kmph
Rationale: DS = 20
US = 4
S = ?
S = (20 - 4)/2 = 8 kmph
Answer: E
Answer: E
Question: The average marks obtained by 120 candidates in a certain examination is 35.Find the total marks.
Options:
A)3800
B)4500
C)5200
D)3400
E)4200
Rationale: Following the above formula, we have the total marks =120*35=4200
Answer is E
Answer: E
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
Options:
A)124432
B)145366
C)157768
D)178432
E)220030
Rationale: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E
Answer: E
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days A do the work if he is assisted by B and C on every third day?
Options:
A)11 days
B)15 days
C)17 days
D)18 days
E)19 days
Rationale: A's 2 day's work = (1/20 * 2) = 1/10
(A + B + C)'s 1 day work = (1/20 + 1/30 + 1/60) = 1/10
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days.
Whole work will be done in (3 * 5) = 15 days.
Answer: B
Answer: B
Question: If 1535/1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?
Options:
A)165/2
B)175/2
C)178/3
D)187 by 2
E)197/2
Rationale: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Answer: D
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)12 cm2
B)30 cm2
C)17 cm2
D)18 cm2
E)19 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle
= 6 * 5 = 30 cm2
Answer:B
Answer: B
Question: There are 9 women and 7 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
Options:
A)432
B)580
C)624
D)756
E)860
Rationale: 9C2 * 7C2 = 36*21 = 756
The answer is D.
Answer: D
Question: The average of 11 numbers is 10.7. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
Options:
A)13.7
B)11.5
C)81.5
D)11.5
E)21.5
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.7 x 11] = 11.5.
Answer: A
Answer: A
Question: If w is 40 percent less than x, x is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?
Options:
A)4%
B)18%
C)36%
D)40%
E)50%
Rationale: Given
w= 0.6x, x=0.6y, z=0.54y,
substituting, w=2/3 Z----> z= 1.5w
and thus z is 50% greater than w.
E is the correct answer.
Answer: E
Question: Look at this series: 98, 98, 90, 90, 82, 82, ... What number should come next?
Options:
A)74
B)15
C)17
D)19
E)11
Rationale: In this series, each number is repeated, then 8 is subtracted to arrive at the next number.
The next number is 74
Answer : 74
Answer: A
Question: Warner Limited has 4 Senior Managing Directors and 6 Managing Directors. Each investment banking deal requires the guidance of three managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Warner Limited possibly provide guidance for?
Options:
A) 116
B) 136
C) 100
D) 200
E) 295
Rationale: P(at least 1 S D) = P(Total) - P(0 Senior Director)
=10C3 - 6C3
= 100
Answer: C
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/2 of the same job. How many days will 10 men and 8 women together take to complete the same job?
Options:
A)6
B)13 1â„2
C)15 3/7
D)Data inadequate
E)None of these
Rationale: 12 M Ã— 18 = 12 W Ã— 18 Ã— 2/1
\ w = 1/2 M
10M + 8W = 10M + 8 Ã— 1/2M = 14 M
\14 men can complete the same work
in 12Ã—18/14=15 3/7days
Answer C
Answer: C
Question: The ages of X and Y are in the ratio of 3:8 respectively and product of their ages is 384. Compute the ratio of their ages three years hence.
Options:
A)3:5
B)2:5
C)3:7
D)3:4
E)1:4
Rationale: as given the ages are of 3x,8x and product of their ages is 384
so, 3x*8x=384
by solving we get 24x^2=384
finally by sloving we get x^2=16
x=4
as given three hence we add 3 for 3x and 4x
we solve it by
3x+4:8x+4
sub x=4 in above ration
we get
15:35
3:7
ANSWER:C
Answer: C
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 20-sided polygon have?
Options:
A) 875
B) 170
C) 1425
D) 2025
E) 2500
Rationale: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 20.
Plugging it in, we get 170 diagonals!
Answer (B).
Answer: B
Question: Adding 50% of x to x is equivalent to multiplying x by which of the following?
Options:
A)12.5
B)1.05
C)1.5
D)1.2
E)1.25
Rationale: 150x/100= 1.5*x
ANSWER:C
Answer: C
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.128 in 4 Years?
Options:
A)5%
B)3%
C)4%
D)9%
E)1%
Rationale: 128 = (800*4*R)/100
R = 4%
Answer: C
Answer: C
Question: A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: I think the order matters so I'm going w/B. I reasoned this one out.
Does "a pair of distinct letters written in alphabetical order" mean anything significant?
1 2 3 4 5 6 7 8 9 10 11 12
A B C D E AA AB AC AD AE BA BB
Answer: B
Question: A and B can do a piece of work in 40 days and 40 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
Options:
A)30days
B)35days
C)40days
D)45days
E)50days
Rationale: Explanation:
(A+B)’s 10 days work = 10[1/40+1/40]=10[1+1/40]= 1/2
A complete remaining work in 1/2*40 = 20
Total work = 10+20 = 30days
Answer: Option A
Answer: A
Question: There are 4 people of different heights standing in order of increasing height. The difference is 2 inches between the first person and the second person, and also between the second person and the third person. The difference between the third person and the fourth person is 6 inches and the average height is 79. How tall is the fourth person?
Options:
A)85
B)87
C)89
D)91
E)93
Rationale: Let x be the height of the first person.
Then the heights are x, x+2, x+4, and x+10.
4x+16 = 4(79) = 316
x = 75 and the fourth person has a height of 75+10 = 85 inches
The answer is A.
Answer: A
Question: Kamal's salary was decreased by 50% and subsequently increased by 30%. How much percent does he lose?
Options:
A)30%
B)37%
C)65%
D)35%
E)45%
Rationale: Explanation :
Solution: let original salary = Rs. 100. new final salary = 130% of (50% of Rs.100) = Rs. (130/100 * 50/100 * 100) = Rs. 65.
.'. Decrease = 35%
Answer : D
Answer: D
Question: A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
Options:
A)9:5
B)9:9
C)9:6
D)9:1
E)9:2
Rationale: Explanation:
Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.
Answer: A) 9:5
Answer: A
Question: A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 99 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?
Options:
A)126 sq. ft
B)64 sq. ft
C)100 sq. ft
D)120 sq. ft
E)140 sq. ft
Rationale: Explanation:
Solution 1
length =9 feet
breadth =37−9/2=14feet
Area =9×14=126 square feet
Answer: Option A
Answer: A
Question: The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Options:
A)279
B)283
C)308
D)318
E)342
Rationale: Other number = (11 x 7700)/275 = 308.
Answer: Option C
Answer: C
Question: What is the equation of a circle of radius 6 units centered at (2, 2)?
Options:
A)x^2 + y^2 + 6x – 4y = 23
B)x^2 + y^2 - 6x + 4y = 23
C)x^2 + y^2 + 6x + 4y = 23
D)x^2 + y^2 - 6x – 4y = - 23
E)x^2 + y^2 - 4x – 4y = 28
Rationale: the equation of a circle with center at (a,b) and radius R is (X-a)^2+(Y-b)^2=R^2
=> answer = (X-2)^2+(Y-2)^2=6^2
solving,,we get the equation in answer choiceE.
Answer: E
Question: The price of sugar is increased by 7%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
Options:
A)(700/107) %
B)(107/100) %
C)(100/107)%
D)(7/100)%
E)(100/700)%
Rationale: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $107.
We want the spendings to remain at $100.
(New consumption)*107 = 100 --> (New consumption) = 100/107 kg.
Percent decrease = Change/Original *100 = (1 - 100/107)/1*100 = 700/107%.
Answer: A.
Answer: A
Question: In how many ways letters of the word RSCUPERATE be arranged?
Options:
A)246577
B)462349
C)454523
D)564656
E)302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: E
Question: 9548 + 7314 = 7362 + (?)
Options:
A)8300
B)8400
C)8500
D)8700
E)9500
Rationale: 9548 16862 = 7362 + x
+ 7314 x = 16862 - 7362
----- = 9500
16862
-----
E)
Answer: E
Question: The current birth rate per thousand is 32, whereas corresponding death rate is 11 per thoudand. The net growth rate in terms of population increase in percent is given by
Options:
A)0.0021%
B)0.021%
C)2.1%
D)21%
E)none
Rationale: Solution
Net growth on 1000 = (32 - 11) = 21.
Net growth on 100
‹=› [21 / 1000 x 100]%
= 2.1%.
Answer C
Answer: C
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)3.6
B)6
C)18
D)24
E)None of these
Rationale: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 432
12R2 = 432
R2 = 36
R = 6.
Answer: Option B
Answer: B
Question: Which of the following describes all values of x for which 4–x^2 >= 0?
Options:
A) x >= 1
B) x <= –1
C) 0 <= x <= 1
D) x <= –1 or x >= 1
E) –2 <= x <= 2
Rationale: 4 - x^2 >=0
means x^2 - 4 <=0
=> (x-2)(x+2) <= 0
=> -2 <= x <= 2
Answer - E
Answer: E
Question: AMS employs 7 professors on their staff. Their respective probability of remaining in employment for 10 years are, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. The probability that after 10 years all 7 of them still work in AMS is ?
Options:
A)0.19
B)0.018144
C)0.1
D)0.16
E)none of these
Rationale: Asking atleast 6 of them continue ,
it has 3 cases.
1 all 7 professors continue.
all 7 continues - 0.3*0.4*.0.5*0.6*0.7*0.8*0.9 =0.018144
B
Answer: B
Question: Jegan has 10 pairs of shoes; each pair is a different color. If Jegan randomly selects 2 shoes without replacement from the 20 shoes, what is the probability that she will select 2 shoes of the same color?
Options:
A)2/15
B)1/41
C)1/35
D)1/12
E)1/19
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 20 shoes = 20/20 = 1
Probability of selecting the next shoe (out of 19 available) having the same color = 1/19 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/19=1/19.
E is the correct answer.
Answer: E
Question: The fourth proportional to 12, 15 and 20 is?
Options:
A)21
B)66
C)25
D)99
E)26
Rationale: (15*20)/12 = 25
Answer: C
Answer: C
Question: If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is:
Options:
A)25%
B)33 1/3 %
C)50%
D)66 2/3 %
E)none
Rationale: Let C.P. of each pen be Re. 1.
Then, C.P. of 8 pens = Rs. 8; S.P. of 8 pens = Rs. 12.
Gain % = 4/8 * 100 = 50%
ANSWER:C
Answer: C
Question: If m/35 is an integer, then each of the following must be an integer EXCEPT
Options:
A)3
B)7/2
C)4
D)5
E)6
Rationale: Now plug m =35 into the answer choices:
A. (35- 28)/7 =1. This is an integer
B. (35+ 21)/7 = 8. This is an integer
C. 14(35)/98 = 7. This is an integer
D. (35^2 - 49)/49 =24. This is an integer
E. (35+ 14)/14 = 7/2. This is NOT an integer
Answer: B
Answer: B
Question: Visitors to show were charged Rs.5 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 2: 5: 13
2x 5x 13x
5 7.5 2.5
10x + 37.5x + 32.5x = 80x/20x
Average = 4
ANSWER:D
Answer: D
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)277
B)299
C)245
D)200
E)211
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.Answer: C
Answer: C
Question: A jar contains 9 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?
Options:
A)1/49
B)1/16
C)1/28
D)1/3
E)1/2
Rationale: Jar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.
Sample space = 9C3 = 84.
Probability of choosing 3 red = 3C3/9C3 = 1/84.
Probability of choosing 3 green = 3C3/9C3 = 1/84.
Probability of choosing 3 blue = 3C3/9C3 = 1/84.
Required probability = 1+1+1/84 = 3/84 = 1/28. Ans (C).
Answer: C
Question: A MAN wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 12 rows the number of trees in each row is 24 if there are 6 more rows find the number of trees in each row?
Options:
A)A)63
B)B)8
C)C)48
D)D)32
E)E)33
Rationale: Required number of trees
= 12/36 * 24= 8.
ANSWER:B
Answer: B
Question: If 2<m<6<m<11, then what is the greatest possible positive integer difference of m and n?
Options:
A)3
B)8
C)5
D)6
E)7
Rationale: Let x=2.1 and y=10.1
Greatest possible difference=10.1-2.1=8
Answer B
Answer: B
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)8 months
B)7 months
C)6 months
D)10 months
E)5 months
Rationale: Let B joined for x months. Then
85000×12:42500×x=3:1
⇒850×12:425x=3:1
⇒850×12×1=3×425x
⇒850×4=425x
⇒x=8
Answer is A.
Answer: A
Question: Every student at Zarcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Zarcy School?
Options:
A)63
B)69
C)74
D)82
E)86
Rationale: total number of students at Zarcy School The answer is 86 or any multiple of 43.E
Answer: E