divelab/Sys2Bench huggingface dataset:
Question: A man, a woman and a boy can complete a job in 3,4 and 12 days respectively.
How many boys must assist 1 man and 1 woman to complete the job in ¼ of a day?
Options:
A)41
B)50
C)22
D)33
E)14
Rationale: (1 man + 1 woman)'s 1 days work = 1/3+1/4=7/12
Work done by 1 man and 1 women n 1/4 day=((7/12)*(1/4))=7/48
Remaining work= 1- 7/48= 41/48
Work done by 1 boy in ¼ day= ((1/12)*(1/4)) =1/48
Therefore, Number of boys required= ((41/48)*48)= 41 days
ANSWER A
Answer: A
Question: Once upon a time in ancient times there was a king who was very found of wines. He had a huge cellar, which had 1000 different varieties of wine all in different caskets (1000 caskets in all). In the adjoining kingdom there was a queen who was envious of the king’s huge wine collection. After some time when she could not bear it any more show conspired to kill her by poisoning all his wine caskets. So she sent one sentry to poison all the caskets, but no sooner had the sentry poisoned only one wine casket, he was caught and killed by the Royal guards. Now the king had a major problem in his hand so as to identify the poisonous casket, which he gave to the Minister. But the situation had two peculiarities.
I: Any one who takes even one drop from the poisonous casket will die.
II: He will die only after one month.
The king also handed over few prisoners to the Minister as “taster” of those caskets, as their lives was of little value.
If the Minister is allowed only 1 month to find out the poisonous casket, what is the minimum number of prisoners he should use as “tasters”?
Options:
A)1023
B)1024
C)1025
D)1026
E)1027
Rationale: Sol:
Study the following table carefully. Each of the prisoners drinks wine from whichever casket has a 1 in his place. If he does not drink there is a 0.
So if no one dies, Casket 1 is poisoned.
If P1 dies, casket 2 is poisoned.
If P1 and P3 die ⇒⇒ casket 6 is poisoned and so on.
So, if there are 3 prisoners, we can differentiate upto 2323 =8 caskets.
So for 1000 caskets [even 1024 caskets], we need only 10 prisoners as 210210 = 1024
Answer B
Answer: B
Question: Three numbers are in the ratio 3:5:7. The largest number is 21. What is the difference between smallest and largest number?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: The three numbers are 3x, 5x, and 7x.
The largest number is 21 = 7*3, so x = 3.
The smallest number is 3*3 = 9.
21 - 9 = 12
The answer is C.
Answer: C
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 42 revolutions, what will be the number of revolutions made by the larger wheel?
Options:
A)15
B)12
C)21
D)9
E)18
Rationale: Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: x : 42
â‡’6Ã—42=14 Ã— x
â‡’x = 18
Answer: Option E
Answer: E
Question: Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000
A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number T of defective chips in a shipment of 60000 chips?
Options:
A)14
B)20
C)22
D)24
E)25
Rationale: I agree with your solution = 20. But the question is:
There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.
The question is to find the expected number T of defective chips, i guess it assume the minimum #, therefore it might not be 20.
Answer: B
Question: The number of new words that can be formed by rearranging the letters of the word 'UP' is ?
Options:
A)1
B)2
C)24
D)520
E)24
Rationale: Number of words which can be formed = 2! - 1
= 2 - 1
= 1.
Answer:A
Answer: A
Question: Mercy's income is 10 percent more than Timothy's income, and Timothy's income is 22 percent less than Ryan's income. What percent of Ryan's income is Mary's income?
Options:
A)81.5%
B)85.5%
C)82.5%
D)84.5%
E)80.5%
Rationale: Ryan's income = 100 (assume);
Timothy's income = 78 (22 percent less than Ryan's income);
Mercy's income = 85.5 (60 percent more than Timothy's income).
Thus, Mercy's income (85.5) is 85.5% of Ryan's income (100).
Answer: B
Answer: B
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 metres) is:
Options:
A)400
B)525
C)750
D)850
E)None
Rationale: Sol.
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 metres.
Then, 2x/60 = 25 ⇔ x = 25 * 60 / 2 = 750
Answer C
Answer: C
Question: 16 men can do a piece of work in 16 days .4 days after they started the work, 8 more men joined them. How many days will they now take to complete the remaining work
Options:
A)7 days
B)8 days
C)9 days
D)10 days
E)None of these
Rationale: Solution:Work done by 1 man in 1 day=1/(16*16)
Work completed by 16 men in 4 days= 4[1/(16*16)]*16=1/4
Remaining work= 1- 1/4= 3/4
Total men now= 16+ 8=24
24 men do 3/4 work
=>24*number of days*Work done by 1 man in 1 day=3/4
=>24*number of days* 1/(16*16)=3/4
=>number of days=8 days
Answer B
Answer: B
Question: A rectangular box measures internally 1.6 m long, 1 m broad and 60 cm deep. The number of cubical blocks each of edge 20 cm that can be packed inside the box is
Options:
A)30
B)60
C)120
D)150
E)None
Rationale: Sol. Number of blocks =
160x100x60
20x20x20] = 120.
Answer C
Answer: C
Question: The present average age of a family of five members is 24 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)
Options:
A)27.5 years
B)17 years
C)17.5 years
D)16.5 years
E)15.5 years
Rationale: Present total age of the members = 24(5) = 120 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 120 -10 = 110 years
Their average age at the time of the birth of the youngest member = [110 - (4 * 10)] / 4 = 17.5 years
ANSWER:C
Answer: C
Question: In a partnership between A, B and C. A's capital is Rs.5500. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)23676
B)19766
C)29172
D)12925
E)11267
Rationale: Explanation:
200 + 130 = 330
800 - 330 = 470
200 ---- 5500
470 ---- ? => 12925
Answer:D
Answer: D
Question: Virginia, Adrienne, and Dennis have taught history for a combined total of 96 years. If Virginia has taught for 9 more years than Adrienne and for 12 fewer years than Dennis, for how many years has Dennis taught?
Options:
A) 23
B) 32
C) 35
D) 41
E) 42
Rationale: Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D
V+A+D = 96
V= A+9
=>A = V-9
V= D-12
=> A = (D-12)-9 = D-21
D-9 + D-21 + D = 96
=> 3D = 96 + 30 = 126
=> D = 42
Answer E
Answer: E
Question: Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Seven years ago Jim was 13 times as old as Sam. How old is Jim now?
Options:
A)8
B)12
C)16
D)20
E)24
Rationale: We're asked how old Jim is NOW. We're given three facts to work with:
1) Today, Jim is TWICE as old as Fred
2) Today, Sam is 2 years younger than Fred
3) 7 years ago, Jim was 13 times as old as Sam.
let's TEST Answer D: 20
IF....Jim is currently 20 years old....
Fred is 10 years old
Sam is 8 years old
7 years ago, Jim was 13 and Sam was 1, so Jim WAS 13 times Sam's age. This is an exact MATCH for what we were told, so this MUST be the answer.
D
Answer: D
Question: In how many different ways can the letters B, E, N, E, F, I, C, I, A, L be arranged?
Options:
A)10×9×8×7×6×5×3×2
B)10×9×8×7×6×5×4×3
C)8!
D)9!
E)10!
Rationale: Number of ways of arranging BENEFICIAL = 10! / 2! * 2! = 10×9×8×7×6×5×3×2. Hence A
Answer: A
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 12 on Wednesday, what would be the value of D calculated on the following Saturday?
Options:
A)2140
B)2520
C)2960
D)3360
E)3710
Rationale: On Saturday, the value would be 7*6*5*12 = 2520
The answer is B.
Answer: B
Question: 4 is what percent of 50?
Options:
A)0.2%
B)8%
C)10%
D)20%
E)500%
Rationale: 4= x*50/100
x = 8%
Ans; B
Answer: B
Question: John purchased a house for Rs.45000 and a site for Rs.25000 respectively, if he sold the house for Rs.55000 and the site for Rs.16000, then find the resultant percentage of gain?
Options:
A)1.39%
B)1.40%
C)1.41%
D)1.42%
E)1.43%
Rationale: Sol.
Total CP = 70000 & total SP = 71000 ⇒ gain = SP/CP = 71000/70000 = 1.0142 = 1.42%.
Answer D
Answer: D
Question: The monthly rent of a shop of dimension 20feet × 18feet is Rs.1440. What is the annual rent per square foot of the shop?
Options:
A)48
B)56
C)68
D)87
E)92
Rationale: Sol. Monthly rent per square feet = 1440/(20*18) = 4
& Annual rent per square feet
=12*4=48
Answer : A
Answer: A
Question: 1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 .........,sum of first 1230 terms of series
Options:
A)2311
B)2411
C)2511
D)2611
E)2487
Rationale: Start with making two series
1+1*2=3 terms 2
1+2*2=5. 3
1+3*2=7. 4
....
....
....
1+47*2=95. 48
1+48*2=97. 49
And last term
1+5*2=11. 6
Total sum= 48(3+97)/2+11=2411
ANSWER:B
Answer: B
Question: A rectangular box of volume Y has width, depth and height in the ratio of 3:2:4 (in that order). What is the height as a function of Y?
Options:
A)(4Y/6)^(1/2)
B)(Y/6)^(1/2)
C)(Y/4)^(1/2)
D)(2Y/3)^(1/2)
E)(Y)^(1/2)
Rationale: We are given width = 3, depth = 2, height = 4.
Then Volume = Width x Depth x Height = 3*2*4 = 24
i.e. Y = 24
The correct option should result in 4 (the height) on substituting the value of Y=24.
Checking options with Y=24:
A) (4Y/6)^(1/2) = (96/6)^(1/2) = 4 CORRECT ANSWER
B) (Y/6)^(1/2) = (24/6)^(1/2) = 2 INCORRECT ANSWER
C) (6Y/4)^(1/2) = (144/4)^(1/2) = 6 INCORRECT ANSWER
D) (Y/3)^(1/2) = (24/3)^(1/2) = 8^(1/2) INCORRECT ANSWER
E) (Y)^(1/2) = (24)^(1/2) INCORRECT ANSWER
Answer: Option A
Answer: A
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?
Options:
A)Rs. 200
B)Rs. 209
C)Rs. 202
D)Rs. 238
E)Rs. 218
Rationale: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 21
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(21 – 20) / 20] * 100
= 5 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 5% p.a.
SI = (PRT/100)
20 = (X*5*2) / 100
X = Rs. 200
ANSWER: A
Answer: A
Question: The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)12N
E)15N
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 300% of 1993:
$500 +2x$500 = $500 + $1000 =$1500
This is 15 times the 1992 number, so the correct answer is 15N.
Answer: E
Question: If n = 8^9 – 8, what is the units digit of n?
Options:
A)4
B)0
C)1
D)2
E)3
Rationale: 8 ^ 9 - 8 = 8 (8 ^ 8 - 1)
==> 8 (2 ^ 24 - 1)
Last digit of 2 ^ 24 is 6 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 6 - 1 = 5 as the unit digit. Now on multiply this with 8, we get unit digit as 0
Answer : B
Answer: B
Question: How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?
Options:
A)55
B)56
C)4
D)5
E)3
Rationale: Solution:
At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60 minute positions].
For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th minute, 48th minute and 60th minute positions.
Hence the difference between the positions of the hour hand and the minute hand will have an integral number of minutes between them.
i.e. 5 positions.
Answer D
Answer: D
Question: A bag contains 4 red, 3 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)1/13
B)2/23
C)1/6
D)4/27
E)3/23
Rationale: P(Both are red),
=4C29C2=4C29C2
=6/36=1/6
C
Answer: C
Question: 20 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence.
Options:
A)19
B)20
C)21
D)22
E)23
Rationale: in case of cycle no of handshakes = no of persons
hence ans = 20
ANSWER:B
Answer: B
Question: In an election between two candidates, the first candidate got 60% of the votes and the second candidate got 240 votes. What was the total number of votes?
Options:
A)400
B)600
C)800
D)1000
E)1200
Rationale: Let V be the total number of votes.
0.4V = 240
V = 600
The answer is B.
Answer: B
Question: In the manufacture of a certain product, 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
Options:
A)0.125%
B)0.2%
C)0.8%
D)1.25%
E)2.0%
Rationale: Percent of defective produced = 5%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(5/100)*100%
= (20/10000)*100%
= (20/100)%
= .2 %
Answer B
Answer: B
Question: The weight of a glass of jar is 10% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?
Options:
A)1/5
B)1/3
C)2/5
D)1/2
E)5/9
Rationale: Let weight of jar filled with beans = 100 g
Weight of jar = 10 g
Weight of coffee beans = 90 g
Weight of jar and remaining beans = 60 g
Weight of remaining beans = 50 g
Fraction remaining = 50/90 = 5/9
Answer is E.
Answer: E
Question: A number is increased by 50 % and then decreased by 50 %. Find the net increase or decrease per cent.
Options:
A)25%
B)18%
C)17%
D)13%
E)16%
Rationale: Let the number be 100.
Increase in the number = 50 % = 50 % of 100
= (50/100 Ã— 100)
= 50
Therefore, increased number = 100 + 50 = 150
This number is decreased by 50 %
Therefore, decrease in number = 50 % of 150
= (50/100 Ã— 150)
= 7500/100
= 75
Therefore, new number = 150 - 75 = 75
Thus, net decreases = 100 - 75 = 25
Hence, net percentage decrease = (25/100 Ã— 100) %
= (2500/100) %
= 25 %
Answer:A
Answer: A
Question: A certain fraction is equivalent to 3/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the sum of the numerator and denominator of the original fraction?
Options:
A) 49
B) 35
C) 28
D) 56
E) 21
Rationale: x/y = 3/5 -> 1
(x+4)/2y = 1/3 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 9/5
=> 10x = 9x + 36
=> x = 36
=> y = 5/3 * 12 = 20
so x + y = 56
The answer is D.
Answer: D
Question: Sonika deposited Rs.6200 which amounted to Rs.7200 after 5 years at simple interest. Had the interest been 3% more. She would get how much?
Options:
A)9680
B)8130
C)8134
D)8556
E)9808
Rationale: (6200*5*3)/100 = 930
7200
--------
8130
Answer: B
Answer: B
Question: From the given choices select the odd man out
Options:
A)37, 14, 19, 8
B)37, 14, 19, 0
C)37, 14, 19, 2
D)37, 14, 19, 7
E)37, 14, 19, 1
Rationale: Explanation:
All the numbers in those options are prime numbers except 14 in option 4.
Answer:D
Answer: D
Question: If x is a positive integer, which of the following must be odd?
Options:
A)x+1
B)x^2+x
C)x^2+x+1
D)x^2−1
E)3x^2−3
Rationale: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: C
Question: If |x – 9/2| = 5/2, and if y is the median of a set of s consecutive integers, where s is odd, which of the following must be true?
I. xys is odd
II. xy(s^2 + s) is even
III. x^2y^2s^2 is even
Options:
A)II only is true
B)III only is true
C)I and III
D)II and III
E)I, II, and III
Rationale: given:
s is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: s = O, y = O and x = O or E
Statement I = x*y*s = y*s*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(s^2 + s) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2s^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.
Answer: A
Question: When the positive integer p is divided by 9, the remainder is 5. What is the remainder when 3p is divided by 9?
Options:
A)0
B)1
C)3
D)4
E)6
Rationale: Lets take the number as p
when p is divided by 9 the remainder is 5 hence p can be written as
p=9k +5
Multiplying by 3 will give
3p = 27k + 15
we can also write
3p = 27k + 9 + 6
Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
Answer: E
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1270. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
Options:
A) 2480
B) 3490
C) 6785
D) 8245
E) 9255
Rationale: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1270, we get the answer of 8245. (ANS D)
Answer: D
Question: Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs 4000, the new ratio becomes 40:57. What is Sumit present salary.
Options:
A)32000
B)34000
C)38000
D)40000
E)None of these
Rationale: Explanation:
Let the original Salaries of Ravi and Sumit is 2x and 3x.
So as per question
2x+4000/3x+4000=40/57
=>57(2x+4000)=40(3x+4000)
=>6x=68000
=>3x=34000
Sumit Salary =3x+4000
34000+4000=38000
Option C
Answer: C
Question: A retailer sold an appliance for $100. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?
Options:
A)$10
B)$16
C)$20
D)$24
E)$25
Rationale: Let P be the original price paid by the retailer.
1.25*P = 100
P = 80
The profit is $20.
The answer is C.
Answer: C
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rohan’s and Sudhir’s share in the profit?
Options:
A)Rs.345
B)Rs.350
C)Rs.352
D)Rs.362
E)Rs.368
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3982 × 1/11 = Rs.362.
D
Answer: D
Question: six friends go to pizza corner where there are different types of pizza available. six different flavours are there and they have to select 2 flavours from 6 flavours.In how many ways they can select?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: 6c2 then ans is 6*5/1*2=15
ANSWER:E
Answer: E
Question: A card player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many hearts as clubs and twice as many diamonds as hearts. How many spades does he hold?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Sol.
The player holds 1 club, 2 hearts and 4 diamonds.
As he holds 13 cards (or seven black cards), it follows that there must be 6 spades.
Answer : A
Answer: A
Question: A certain bag contains 100 balls — 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
Options:
A)0.9
B)0.75
C)0.6
D)0.8
E)0.5
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 10)/100 = 90/100 = 0.9.
Answer is A
Answer: A
Question: y and z represents 2 gas stations which are 270 km apart. if two cars leave each gas station and drive towards each other, at what time will they meet each other given that the first car left the gas station at 10 a.m. and travels at a speed of 75 kmph while the second car left the station at 11 a.m. and travels at a speed of 55 kmph.
Options:
A)12.00 p.m
B)11.30 p.m
C)2.30 p.m
D)12.30 p.m
E)1.30 p.m
Rationale: Suppose they meet x hours after 10 a.m.
Distance moved by first car in x hours + distance moved by 2nd car in x-1 hrs = 270
75x+55(x-1) = 270
75x+55x-55= 270
130x= 325
x = 2.5
So they meet 2.5 hr after 10 a.m. which is at 12.30 p.m.
Answer is D
Answer: D
Question: What should come in place of question mark (?) in the following equation?
5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = ?
Options:
A)7
B)8 1⁄2
C)7 1⁄2
D)6 1⁄2
E)None of these
Rationale: ? = 5 3⁄5 ÷ 3 11⁄15 + 5 1⁄2 = 28⁄5 ÷ 56⁄15 + 11⁄2
= 28⁄5 × 15⁄56 + 11⁄2 = 3⁄2 + 11⁄2 = 14⁄2 = 7
Answer A
Answer: A
Question: The cost of 2 chairs and 3 tables is Rs.1500. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
Options:
A)228
B)287
C)277
D)188
E)300
Rationale: Explanation:
2C + 3T = 1500 --- (1)
3C + 2T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 300 => T - C = 300
Answer:E
Answer: E