RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A retail item is offered at a discount of b percent (where b > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of b, would result in the same final price?
A.b+5/1.05
B.b/1.05 +5
C.1.05b-5
D.b-5/1.05
Answer: C.1.05b-5
Explanation: Let x be the price of the item.
Final price after discount and sales tax = x * (1 - b/100) * 1.05
Let c be the percent discount which would result in the same final price.
Then,
x * (1 - b/100) * 1.05 = x * (1 - c/100)
=> 1.05 - 1.05b/100 = 1 - c/100
=> c/100 = 1.05b/100 - .05
=> c = 1.05b - 5
Hence ,option C is correct.
Question: A train 1600 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 60 sec. The speed of the train is?
A.42 km/hr
B.44 km/hr
C.46 km/hr
D.48 km/hr
Answer: A.42 km/hr
Explanation: Speed of the train relative to man = 1600/60 = 80/6 m/sec.
= 80/6 * 18/5 = 48 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 6 = 48 => x = 42 km/hr.
Answer: A
Question: What is the area of a square field whose diagonal of length 20 m?
A.288
B.289
C.200
D.112
Answer: C.200
Explanation: d2/2 = (20 * 20)/2
= 200
Answer: C
Question: How many times are the hands of a clock at right angle in a day?
A.22
B.24
C.44
D.48
Answer: C.44
Explanation: EXPLANATION
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer C
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is
A.5/6
B.5/9
C.5/5
D.5/2
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.Answer: B
Question: If 0.5% of A =70 paise, then the value of A is ?
A.Rs. 170
B.Rs. 140
C.Rs. 1.70
D.Rs. 4.25
Answer: B.Rs. 140
Explanation: Answer
∵ 0.5/100 of A = 70/100
∴ A = Rs. (70 / 0.5) = Rs. 140
Correct Option: B
Question: Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/5, what is the value of X/Y ?
A.3.
B.5
C.1/2.
D.1/3.
Answer: B.5
Explanation: Answer is B : 5
X - Y = (X + Y)/2
Solving for X/Y = 5
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
A.348
B.277
C.960
D.872
Answer: C.960
Explanation: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: C
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
A.33 1/8%
B.33 9/3%
C.33 1/3%
D.93 1/3%
Answer: C.33 1/3%
Explanation: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Question: |x+3| – |4-x| = |9+x| How many solutions will this equation have?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: You have |x+3| - |4-x| = |8+x|
First, look at the three values independently of their absolute value sign, in other words:
|x+3| - |4-x| = |8+x|
(x+3) - (4-x) = (8+x)
Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.
when x=-10
I.) (x+3)
(-10+3)
(-7)
II.) (4-x)
(4-[-10]) (double negative, so it becomes positive)
(4+10)
(14)
III.) (8+x)
(8+-10)
(-2)
In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.
Here is how I do it step by step.
I.) |x+3| - |4-x| = |8+x|
II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:
(x+3)
x=-3
(-3+3) = 0
(4-x)
x=4
(4-4) = 0
(8+x)
x=-8
(8+-8) = 1
B