What are the total number of five-digit numbers divisible by 5, that can be formed by using digits 1, 2, 3, 4, and 5, such that no digit is repeated?
Anonymous Quiz
21%
(a) 120
10%
(b) 8
63%
(c) 24
6%
(d) 36
π6
πAns. C | Explanation:
As the number is divisible by 5, so the unit place will always be 5.
The rest of the four positions may be filled by the remaining 4 digits as follows:
* Tens place in 4 ways
* Hundreds place in 3 ways
* Thousands place in 2 ways
* Ten Thousands place in 1 way
Hence, total number of required numbers = 4 Γ 3 Γ 2 Γ 1 = 24
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As the number is divisible by 5, so the unit place will always be 5.
The rest of the four positions may be filled by the remaining 4 digits as follows:
* Tens place in 4 ways
* Hundreds place in 3 ways
* Thousands place in 2 ways
* Ten Thousands place in 1 way
Hence, total number of required numbers = 4 Γ 3 Γ 2 Γ 1 = 24
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π7
In a city, 20% families read only two newspapers, 40% of the remaining read three newspapers and the remaining families read only one newspaper. Which of the following statements must definitely be true?
Anonymous Quiz
6%
(a) Only 20% of the total families read three newspapers.
53%
(b) 48% of the total families read only one newspaper.
35%
(c) 60% of the total families read at least two newspapers.
6%
(d) 88% of the total families read at least one newspaper.
π5
πAns. B | Explanation:
Let total number of families be 100.
Then, number of families reading only 2 newspapers = 20
Number of families reading 3 newspapers = 40% of (100 β 20) = 40% of 80 = 32
Number of families reading only 1 newspaper = 100 β (20 + 32) = 100 β 52 = 48
Thus, 48% of the total families read only one newspaper.
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Let total number of families be 100.
Then, number of families reading only 2 newspapers = 20
Number of families reading 3 newspapers = 40% of (100 β 20) = 40% of 80 = 32
Number of families reading only 1 newspaper = 100 β (20 + 32) = 100 β 52 = 48
Thus, 48% of the total families read only one newspaper.
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π6
A street vendor has enough money to buy 20 pairs of shoes. If he gets discount of Rs. 25 on each pair of shoe, then he can buy two more pairs of shoes, and still have Rs. 70 left with him. How much money did he have originally?
Anonymous Quiz
11%
(a) Rs. 4500
73%
(b) Rs. 4800
13%
(c) Rs. 5000
2%
(d) Rs. 5200
π5
πAns. B | Explanation:
Let the original price of each pair of shoe be Rs. x.
According to the question,
20x = 22(x β 25) + 70
or, 20x = 22x β 550 + 70
or, 22x β 20x = 480
or, 2x = 480
or, x = Rs. 240
So, the amount of money that street vendor originally had = 20x = 20 Γ 240 = Rs. 4800
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Let the original price of each pair of shoe be Rs. x.
According to the question,
20x = 22(x β 25) + 70
or, 20x = 22x β 550 + 70
or, 22x β 20x = 480
or, 2x = 480
or, x = Rs. 240
So, the amount of money that street vendor originally had = 20x = 20 Γ 240 = Rs. 4800
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π7
In a certain code language, βNOTEβ is coded as βMONPSUDFβ. How will βROADβ be coded as in that language?
Anonymous Quiz
66%
(a) QSNPZBCE
15%
(b) QSMPZBCE
11%
(c) QSNQZBCE
7%
(d) QSNPYBCE
π6
How many pairs of digits in the number 543968 have as many numbers between them as in the series of natural numbers (consider both backward and forward directions)?
Anonymous Quiz
12%
(a) Only one
42%
(b) More than one but less than three
38%
(c) More than three
9%
(d) Only three
π1
A is the mother of B. B is the sister of C. D is the son of C. E is the brother of D. F is the mother of E. G is the granddaughter of A. H has only two children - B and C. How is C related to E?
Anonymous Quiz
42%
(a) Father
24%
(b) Son
23%
(c) Mother
11%
(d) Cousin
π8β€1
Which number will replace the question mark (?) in the following series?
A 0, D 5, H 15, M 30, S 50, ?
A 0, D 5, H 15, M 30, S 50, ?
Anonymous Quiz
14%
(a) A 75
16%
(b) A 65
60%
(c) Z 75
10%
(d) Z 85
π11
Four wooden sticks of lengths 85 cm, 119 cm, 136 cm and 204 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?
Anonymous Quiz
6%
(a) 36
67%
(b) 32
20%
(c) 30
7%
(d) 35
π1π₯1
πAns. B | Explanation:
Since each stick must be cut into parts of equal length and each part must be as long as possible. So, we need to find out the HCF.
HCF of 85, 119, 136 and 204 = 17
Number of parts from 85 cm long stick = 85/17 = 5
Number of parts from 119 cm long stick = 119/17 = 7
Number of parts from 136 cm long stick = 136 /17 = 8
Number of parts from 204 cm long stick = 204 /17 = 12
β΄ Maximum number of pieces = 5 + 7 + 8 + 12 = 32
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Since each stick must be cut into parts of equal length and each part must be as long as possible. So, we need to find out the HCF.
HCF of 85, 119, 136 and 204 = 17
Number of parts from 85 cm long stick = 85/17 = 5
Number of parts from 119 cm long stick = 119/17 = 7
Number of parts from 136 cm long stick = 136 /17 = 8
Number of parts from 204 cm long stick = 204 /17 = 12
β΄ Maximum number of pieces = 5 + 7 + 8 + 12 = 32
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π7
Dr. Bunti made a medicine by mixing two herbs X and Y. In 50 g of that medicine, the percentage of herb X is 40%. How much of herb X should Dr. Bunti add into it further so as to increase its percentage to 84%?
Anonymous Quiz
12%
(a) 142 g
23%
(b) 132.8 g
59%
(c) 137.5 g
7%
(d) 141.7 g
π3
πAns. C | Explanation:
According to the question,
Quantity of herb X in 50 g of medicine = (40/100) Γ 50 = 20 g
Let x g of herb X is further mixed in the medicine.
Then, [(20 + x)/(50 + x)] Γ 100 = 84
Or 2000 + 100x = 4200 + 84x
Or 16x = 2200
Or x = 2200/16
Or x = 137.5 g
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According to the question,
Quantity of herb X in 50 g of medicine = (40/100) Γ 50 = 20 g
Let x g of herb X is further mixed in the medicine.
Then, [(20 + x)/(50 + x)] Γ 100 = 84
Or 2000 + 100x = 4200 + 84x
Or 16x = 2200
Or x = 2200/16
Or x = 137.5 g
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π3β€1
A faulty clock was set correct at 6:00 a.m. on Thursday. This clock gains 5 seconds in every 5 minutes. What must be the approximate time displayed by this clock at 5:30 p.m. on the same day?
Anonymous Quiz
53%
(a) 5:41 p.m.
20%
(b) 5:13 p.m.
19%
(c) 5:23 p.m.
7%
(d) 5:56 p.m.
π3
πAns. A | Explanation:
Total time from 6 a.m. to 5:30 p.m. = 11 hours 30 minutes = 690 minutes
Clock gains 5 seconds in every 5 minutes.
β΄ Gain in 1 minute = 5/5 = 1 second
β΄ Gain in 60 minutes = 60 Γ 1 = 60 seconds
β΄ Gain in 690 minutes = 690 seconds = 690/60 minutes = 69/6 minutes = 23/2 minutes = 11.5 minutes OR 11 minutes 30 seconds
Hence, the correct time = 5:30 + 0:11 = 5:41 p.m. (approximately)
(as the clock is gaining time, it means it is running faster than it should and hence display time will be more than the real time)
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Total time from 6 a.m. to 5:30 p.m. = 11 hours 30 minutes = 690 minutes
Clock gains 5 seconds in every 5 minutes.
β΄ Gain in 1 minute = 5/5 = 1 second
β΄ Gain in 60 minutes = 60 Γ 1 = 60 seconds
β΄ Gain in 690 minutes = 690 seconds = 690/60 minutes = 69/6 minutes = 23/2 minutes = 11.5 minutes OR 11 minutes 30 seconds
Hence, the correct time = 5:30 + 0:11 = 5:41 p.m. (approximately)
(as the clock is gaining time, it means it is running faster than it should and hence display time will be more than the real time)
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π5
If Ξ± and Ξ² are two real numbers such that Ξ± + Ξ² = - q/p and Ξ±Ξ² = r/p, where 0<p<q<r (p, q, r are natural numbers), then which one of the following alternatives represents the highest value?
Anonymous Quiz
6%
(a) 1 / (Ξ± + Ξ²)
37%
(b) (1/ Ξ±) + (1/ Ξ²)
47%
(c) β 1/ (Ξ±Ξ²)
10%
(d) Ξ±Ξ²/(Ξ± + Ξ²)
π2
πAns. C | Explanation:
It is given that Ξ± + Ξ² = - q/p and Ξ±Ξ² = r/p, where 0<p<q<r
So, letβs assume p = 1, q = 2 and r = 3.
Putting these values in answer options, we get
(A) 1 / (Ξ± + Ξ²) = - p/q = - (1/2)
(B) (1/ Ξ±) + (1/ Ξ²) = (Ξ± + Ξ²)/ Ξ±Ξ² = -(q/p) Γ (p/r) = - (q/r) = - (2/3)
(C) β 1/ (Ξ±Ξ²) = -(p/r) = - (1/3)
(D) Ξ±Ξ²/(Ξ± + Ξ²) = r/p Γ (-p/q)= - r/q = - (3/2)
We can see that, - (1/3) is the greatest among the above values.
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It is given that Ξ± + Ξ² = - q/p and Ξ±Ξ² = r/p, where 0<p<q<r
So, letβs assume p = 1, q = 2 and r = 3.
Putting these values in answer options, we get
(A) 1 / (Ξ± + Ξ²) = - p/q = - (1/2)
(B) (1/ Ξ±) + (1/ Ξ²) = (Ξ± + Ξ²)/ Ξ±Ξ² = -(q/p) Γ (p/r) = - (q/r) = - (2/3)
(C) β 1/ (Ξ±Ξ²) = -(p/r) = - (1/3)
(D) Ξ±Ξ²/(Ξ± + Ξ²) = r/p Γ (-p/q)= - r/q = - (3/2)
We can see that, - (1/3) is the greatest among the above values.
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π2
What is the ratio of expected police-to-population ratio of West Bengal, Bihar and Andhra Pradesh taken together to the existing police-to-population ratio of Uttar Pradesh, Andhra Pradesh and Maharashtra taken together?
Anonymous Quiz
47%
(a) 2962 : 2955
22%
(b) 331 : 297
21%
(c) 93 : 97
11%
(d) 5920 : 6131
π5
πAns. A | Explanation:
Expected police-to-population ratio of West Bengal = 1187
Expected police-to-population ratio of Bihar = 1133
Expected police-to-population ratio of Andhra Pradesh = 642
Existing police-to-population ratio of Uttar Pradesh = 1173
Existing police-to-population ratio of Andhra Pradesh = 953
Existing police-to-population ratio of Maharashtra = 829
Required ratio = [(1187 + 1133 + 642)/ (1173 + 953 + 829)] = 2962/2955 = 2962 : 2955
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Expected police-to-population ratio of West Bengal = 1187
Expected police-to-population ratio of Bihar = 1133
Expected police-to-population ratio of Andhra Pradesh = 642
Existing police-to-population ratio of Uttar Pradesh = 1173
Existing police-to-population ratio of Andhra Pradesh = 953
Existing police-to-population ratio of Maharashtra = 829
Required ratio = [(1187 + 1133 + 642)/ (1173 + 953 + 829)] = 2962/2955 = 2962 : 2955
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π3β€1