{"id":11790,"date":"2018-03-02T14:43:30","date_gmt":"2018-03-02T09:13:30","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=11790"},"modified":"2019-04-29T15:56:45","modified_gmt":"2019-04-29T10:26:45","slug":"cat-questions-last-two-digits","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-questions-last-two-digits\/","title":{"rendered":"CAT Questions on Last Two Digits"},"content":{"rendered":"

CAT Questions on Last Two Digits:<\/strong><\/span><\/h1>\n

Download CAT Questions on Last Two Digits<\/a><\/p>\n

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

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

Question 1:<\/strong> If the last two digits of (1!+2!+3!….. 50!) are ab, then find the value of a*b?<\/p>\n

a) 3
\nb) 4
\nc) 5
\nd) 6<\/p>\n

Question 2:<\/strong> Find the last two non-zero digits of 25!.<\/p>\n

a) 74
\nb) 94
\nc) 84
\nd) 64<\/p>\n

Question 3:<\/strong> Find the sum of the last two digits in $89^{82}$.<\/p>\n

a) 1
\nb) 3
\nc) 5
\nd) 7<\/p>\n

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

<\/a><\/div>\n

Question 4:<\/strong> What are the last two digits of the sum $(19!)^2 + (18!)^2 + (17!)^2 + \u2026\u2026\u2026(0!)^2$<\/p>\n

a) 33
\nb) 34
\nc) 17
\nd) 18<\/p>\n

Question 5:\u00a0<\/strong>Find the last two digits of the number $27^{103}$?<\/p>\n

a) 63
\nb) 73
\nc) 93
\nd) 83<\/p>\n

Solutions for\u00a0CAT Questions on Last Two Digits:<\/strong><\/span><\/p>\n

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

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

Lat two digits is nothing but the remainder with 100
\nFrom 10! onwards all terms will be divisible by 100
\nSo we just need to find out the remainder of (1! + 2! + ….9! ) with 100
\nSo on calculating the remainders we get,
\n1+2+6+24+20+20+40+20+80 = 213,
\n213mod 100 = 13, so last two digits are 13
\nHence the product of digits is 1*3 = 3<\/p>\n

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

The last two non-zero digits of the factorial of a number X, which is divisible by 5 can be calculated as below.
\nlast two non-zero digits of X! = last two non zero digits of $[x\/5]! * 12^{x\/5}$
\nHere x = 25. ==> $[25\/5]! *12^{25\/5}$ = $5!*12^{5}$ = 120*32 (last two digits of $12^5$ is 32) ==> 84
\nTherefore last two digits of 25! = 84.<\/p>\n

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

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

Last two digits can be found by finding the remainder with 100.
\n$89^{82}=(90-1)^{82}$
\n$=(…00)-(82\\times90)+1$
\n$=(…00)-7380+1$
\n$=(…00)-7379$
\n$=(…21)$
\nSo the last two digits are 21.
\nSum of digits = 3<\/p>\n

<\/a><\/div>\n

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

From $(5!)^2$ to $(19!)^2$ every number in the series ends with \u201800\u2019.
\nNow we need to calculate the sum of last two digits of numbers from $(0!)^2$ to $(4!)^2$ = 1 + 1 + 4 + 36 + 576 = 618
\nTherefore last two digits of the sequence are 18.<\/p>\n

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

Last two digits of a number is nothing but the remainder when the number is divided by 100. So we essentially have to find the remainder when the given number is divided by 100.
\n$27^{103}$ mod 100
\n100 can be written as 25*4
\n$27^{103}$ mod 4 = $(-1)^{103}mod4 = -1 = 3$
\n$27^{103}$mod 25 = $2^{103}$mod25 = $(2^{10})^{10}*8$mod25
\n= $(1024)^{10}*8$mod25 = 1*8 = 8
\nThus the required remainder is of the form
\n4k+3 = 25m+8
\nIf m = 1, we get 33 but this is not of the form 4k+3. Hence this is not possible.
\nIf m = 2, we get 58 but this is again not of the form 4k+3. Hence this is also not possible.
\nm=3 gives 83. This is of the form 4k+3. Hence the required remainder is 83.<\/p>\n

Take a free CAT online mock test<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

CAT Questions on Last Two Digits: Download CAT Quant Questions PDF Take Free Mock Test for CAT Question 1: If the last two digits of (1!+2!+3!….. 50!) are ab, then find the value of a*b? a) 3 b) 4 c) 5 d) 6 Question 2: Find the last two non-zero digits of 25!. a) 74 […]<\/p>\n","protected":false},"author":21,"featured_media":11796,"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":[422],"class_list":{"0":"post-11790","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-2018"},"better_featured_image":{"id":11796,"alt_text":"CAT Questions on Last Two Digits","caption":"CAT Questions on Last Two Digits","description":"CAT Questions on Last Two 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