{"id":11838,"date":"2022-03-03T13:07:07","date_gmt":"2022-03-03T07:37:07","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=11838"},"modified":"2022-08-04T09:27:34","modified_gmt":"2022-08-04T03:57:34","slug":"cat-questions-base-system","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-questions-base-system\/","title":{"rendered":"CAT Questions on Base System"},"content":{"rendered":"

CAT Questions on Base System:<\/strong><\/span><\/p>\n

Download CAT Questions on Base System<\/a><\/p>\n

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Download CAT Quant Questions PDF<\/a><\/p>\n

Take Free Mock Test for CAT<\/a><\/p>\n

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Question 1:\u00a0<\/strong>$$(245)_{x}+(162)_{x}-(427)_{x}=0$$ in some base x. What is the value of x?<\/p>\n

a) 8
\nb) 9
\nc) 10
\nd) Cannot be determined<\/p>\n

Question 2:\u00a0<\/strong>What will be the number of zeroes in$$ (2000!)_{34}$$. Here 34 is the base in which the number is written.<\/p>\n

a) 122
\nb) 123
\nc) 124
\nd) 125<\/p>\n

Question 3:\u00a0<\/strong>A two digit number A in base 11 is one-third of the number formed by reversing its digits when considered in base 19. How many such numbers are possible?<\/p>\n

a) 5
\nb) 6
\nc) 7
\nd) 8<\/p>\n

Question 4:\u00a0<\/strong>How many 3 digit numbers in decimal system are 3 digit numbers in both base 9 and base 11?<\/p>\n

a) 625
\nb) 507
\nc) 528
\nd) 608<\/p>\n

Download CAT 2022 Syllabus PDF<\/a><\/p>\n

Question 5:\u00a0<\/strong>How many 1s exist in the binary equivalent of the decimal number 93640?<\/p>\n

a) 6
\nb) 7
\nc) 8
\nd) 9<\/p>\n

Solutions for\u00a0CAT Questions on Base System:<\/strong><\/span><\/p>\n

Solutions:<\/strong><\/p>\n

1) Answer (A)<\/strong><\/p>\n

$$(245)_{x}+(162)_{x}-(427)_{x}=0$$
\n$$=>(2x^2+4x+5)+(x^2+6x+2)-(4x^2+2x+7)=0$$
\n$$=>x^2-8x=0$$
\n$$=>x=8$$<\/p>\n

2) Answer (B)<\/strong><\/p>\n

34 = 17*2
\nSo we have to find the highest power of 17 in 2000!. We need not find the power of 2 because of 2 will be greater than the power of 17. Thus the power of 17 will act as the limiting value.
\nThus the highest power of 17 in 2000! is
\n[2000\/17] + [ 2000\/289] + [2000\/4913], [] is greatest integer function
\n= 117 + 6 + 0 = 123
\nThus the required number of zeroes is 123.<\/p>\n

3) Answer (A)<\/strong><\/p>\n

Let the number be xy.
\n=> $$(xy)_{11}=\\frac{1}{3}(yx)_{19}$$
\n=> $$y+11x=\\frac{1}{3}(x+19y)$$
\n=> $$3y+33x=x+19y$$
\n=> $$32x=16y$$ or $$2x=y$$
\nSo, (x,y) can be (2,1)(4,2)(6,3)(8,4)(10,5)
\nNumbers such as 10, 11, 12.. etc. are represented as alphabets a,b,c etc in higher bases. Thus, the case of (10,5) also satisfies our requirements.
\nThe next pair (12,6) can\u2019t be considered since 12 is not a single digit number in base 11 and thus, all other cases greater than (10,5) can be excluded.
\nThus, the answer is 5.<\/p>\n

Preparation tips for CAT – Beginners<\/a><\/p>\n

How to prepare for CAT by Self-Study<\/a><\/p>\n

4) Answer (D)<\/strong><\/p>\n

Smallest 3 digit numbers in base 9 is $$1*9^{2} + 0* 9 + 0* 9^{0} = 81$$, Largest 3 digit number in base 9 is $$8*9^{2} + 8*9 + 8*9 = 728$$
\nSmallest 3 digit number in base 11 is is $$1*11^{2} + 0* 11 + 0* 11^{0} = 121$$
\nLargest 3 digit number in base 11 is $$10*11^{2} + 10*11 + 10*11^{0}= 1330$$
\nSo 3 digit numbers in base 10 which are also 3 digit numbers in base 9 and base 11 are
\nfrom 121 to 728 = 608<\/p>\n

5) Answer (D)<\/strong><\/p>\n

On prime factorizing the number 93640 with 2, we will get the binary equivalent of the number.<\/p>\n

We know that the binary equivalent of 5 is 101.
\nHence, we get the binary equivalent as 10110110111001000.
\nHence, there are 9 1s.<\/p>\n

Take a free CAT online mock test<\/a><\/p>\n

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CAT Questions on Base System: Download CAT Quant Questions PDF Take Free Mock Test for CAT CAT Holi Offer – Use coupon “HOLI30” Question 1:\u00a0$$(245)_{x}+(162)_{x}-(427)_{x}=0$$ in some base x. What is the value of x? a) 8 b) 9 c) 10 d) Cannot be determined Question 2:\u00a0What will be the number of zeroes in$$ (2000!)_{34}$$. […]<\/p>\n","protected":false},"author":21,"featured_media":11844,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125],"tags":[5119],"class_list":{"0":"post-11838","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-featured","10":"tag-cat-2022"},"better_featured_image":{"id":11844,"alt_text":"CAT Questions on Base System","caption":"CAT Questions on Base System","description":"CAT Questions on Base 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