# (01 NOV 2020) – Logical Reasoning, 1st & 2nd Shift NTA UGC NET JRF Question paper, Answer key

1. The difference between the squares of two consecutive numbers is 35. The smaller number is:

(1) 14
(2) 15
(3) 16
(4) 17

Explanation: Let’s get the two numbers as X and (X+1).
(X+1)²−X²=35
(X²+2X+1)−X²=35
2X+1=35 ; 2X=34 ; X=17

2. Given below are two statements.
Statement I: If an article is sold at a gain of 19%, then selling price is 109% of cost price.
Statement II: If an article is sold at a loss of 9%, then selling price is 109% of cost price.
In the light of the above statements, choose the most appropriate answer from the options given below:

1 Both Statement I and Statement II are correct
2 Both Statement I and Statement II are incorrect
3 Statement I is correct but Statement II is incorrect
4 Statement I is incorrect but Statement II is correct
नीचे दो कथन दिए गए हैं।
कथन I: यदि कोई वस्तु 19% के लाभ पर बेची जाती है, तो विक्रय मूल्य क्रय मूल्य का 109% है।
कथन II: यदि कोई वस्तु 9% की हानि पर बेची जाती है, तो विक्रय मूल्य क्रय मूल्य का 109% होता है।
उपरोक्त कथनों के आलोक में, नीचे दिए गए विकल्पों में से सबसे उपयुक्त उत्तर का चयन करें:

Explanation: If sold at 19% gain, It should be 100% + 19% = 119%
If sold at 9% loss, It should be 100% – 9% = 91%

3. Given below are two statements.
Statement I: A number is divisible by 3, if the sum of its digits is divisible by 3.
Statement II: A number is divisible by 9, if the sum of its digits is not divisible by 9.
In the light of the above statements, choose the most appropriate answer from the options given below:

1 Both Statement I and Statement II are correct
2 Both Statement I and Statement II are incorrect
3 Statement I is correct but Statement II is incorrect
4 Statement I is incorrect but Statement II is correct
कथन I: कोई संख्या 3 से विभाज्य होती है, यदि उसके अंकों का योग 3 से विभाज्य हो।
कथन II: एक संख्या 9 से विभाज्य है, यदि उसके अंकों का योग 9 से विभाज्य नहीं है।
उपरोक्त कथनों के आलोक में, नीचे दिए गए विकल्पों में से सबसे उपयुक्त उत्तर का चयन करें:

Explanation: It is divisibility Rule of 3 and 9.
For 9 it is divisible with 9 if its sum is divisible by 9.
Example: Sum of number 729 = 7 + 2 + 9 = 18 and 18 comes in 9 table so 729 also divisible with 9

4. A train, 130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is :

A. 245 metres
B. 235 metres
C. 270 metres
D. 220 metres
130 मीटर लंबी एक ट्रेन 45 किमी/घंटा की गति से यात्रा करती है और एक पुल को 30 सेकंड में पार करती है। पुल की लंबाई है:

Explanation: Speed = 45 km/hr = 45 × 5/ 18 m/s = 12.5 m/s
Time = 30 s
Distance travelled = 12.5 × 30 = 375 m
Length of the bridge = 375 − 130 = 245 m

5. Complete the series : 2,5, 9, 19, 37, …

A. 75
B. 77
C. 76
D. 78

Explanation: 2*2+1=5, 5*2-1=9, 9*2+1=19,
19*2-1=37, 37*2+1=75.

6. Statement I: It is possible that there are 53 Tuesdays in a non-leap year.
Statement II : In a non-leap year, there are 54 of each day plus one extra day.

A. Both Statement I and Statement II are true
B. Both Statement I and Statement II are false
C. Statement I is correct but Statement II is false
D. Statement I is incorrect but Statement II is true
कथन I: यह संभव है कि एक गैर-लीप वर्ष में 53 मंगलवार हों।
कथन II: एक गैर-लीप वर्ष में, प्रत्येक दिन के 54 और एक अतिरिक्त दिन होते हैं।

Explanation: Statement I: In general year there is 1 odd day
(General year: No. of days- 365, Feb- 28, 52 weeks & 1 odd day) So any day can be 53 in a year
Statement II: All days cannot be 54 days as total days can be 365

7. Kavitha collected 8 spiders (with 8 legs each) and beetles (with 6 legs each). When she counted the legs, she found that there were altogether 54. Which of the following is/are true?
A. She collected 5 spiders
B. She collected 3 spiders
C. She collected 5 beetles
D. She collected 3 beetles

(1) (A) and (C) only
(2) (A) and (D) only
(3) (B) and (D) only
(4) (B) and (C) only
कविता ने 8 मकड़ियाँ (प्रत्येक में 8 टाँगों वाली) और भृंगों (प्रत्येक 6 टाँगों वाली) को इकट्ठा किया। जब उसने टाँगों की गिनती की, तो उसने पाया कि कुल मिलाकर 54 थे। निम्नलिखित में से कौन-सा/से सत्य है/हैं?

Explanation: Each spider has 8 legs and the beetle has 6 legs.
Let us start with all 8 spiders. In that case, there would be a total of 64 legs. Replacing one spider by a beetle will reduce 2 legs. We need to reduce 10 legs to have a total of 54 legs. So, we need to replace 5 spiders with 5 beetles.
Spiders: 3
Beetles: 5
Total legs for spiders: 3×8=24
Total legs for beetles: 5×6=30
Total legs =24+30=54 .

8. The average of seven consecutive numbers is 33. The largest of these numbers is:

(1) 39
(2) 34
(3) 36
(4) 38
लगातार सात संख्याओं का औसत 33 है। इनमें से सबसे बड़ी संख्या है:

Explanation: (x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6))/7=33
7x+21=7*33; 7x=231-21
7x=210; x=30
largest is x+6=30+6=36

9. At what time between 2 and 3 ‘o clock will the hour hand and minute hand of a clock come together?

A. 10+ 11/10 min. past 2
B. 10+ 10/11 min. past 2
C. 11+ 10/11 min. past 2
D. 11+ 10/11 min. past 2
2 से 3 बजे के बीच किस समय घड़ी की घण्टे की सूई और मिनट की सूई एक साथ आयेगी?

Explanation: Degree Angle= 30 Hr – 11/2 Minute
0= 30 x 2 -11/2M
-60= -11/2M
M= 120/11=1x 10/11

10. In a class of 65 students, 27 speak Hindi, 21 speak English and 17 speak Bangla. 7 speak only English and Hindi, 6 speak only Hindi and Bangla and 5 speak only English and Bangla. If 12 speak only Hindi then how many speak all the three languages?

(1) 5
(2) 4
(3) 3
(4) 2
65 छात्रों की एक कक्षा में, 27 हिंदी बोलते हैं, 21 अंग्रेजी बोलते हैं और 17 बांग्ला बोलते हैं। 7 केवल अंग्रेजी और हिंदी बोलते हैं, 6 केवल हिंदी और बांग्ला बोलते हैं और 5 केवल अंग्रेजी और बांग्ला बोलते हैं। यदि 12 केवल हिन्दी बोलते हैं, तो कितने लोग तीनों भाषाएँ बोलते हैं?