{"id":2627,"date":"2018-02-08T15:51:40","date_gmt":"2018-02-08T10:21:40","guid":{"rendered":"http:\/\/iquanta.in\/blog\/?p=2627"},"modified":"2021-12-31T13:07:16","modified_gmt":"2021-12-31T07:37:16","slug":"past-cat-remainder-questions","status":"publish","type":"post","link":"https:\/\/www.iquanta.in\/blog\/past-cat-remainder-questions\/","title":{"rendered":"Past CAT Remainder Questions"},"content":{"rendered":"

So we have this biggest community for CAT Preparation, and we discuss almost everything about CAT here in this group called CAT Preparation – iQuanta<\/a> .Anyone can be a part of it by sending a join request.<\/p>\n

So here are few variety of questions on Past CAT Remainder Questions, discussed in group along with detailed solutions.<\/p>\n

1.What is the remainder when 4^96 is divided by 6?<\/strong><\/p>\n

1) 0
\n2) 2
\n3) 3
\n4) 4<\/p>\n

Remark:<\/strong> It can be done in 3 different ways, iQuanta shortcut, or Euler or Chinese remainder Theorem<\/p>\n

Solution here: https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226230407544659\/<\/a><\/strong><\/p>\n

2. The remainder, when (15^23 + 23^23) is divided by 19, is:<\/strong><\/p>\n

1) 4
\n2) 15
\n3) 0
\n4) 18<\/p>\n

Remark : It uses\u00a0\"\"<\/p>\n

Solution here:\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226238654210501\/<\/a><\/p>\n

3. If x = (16^3 + 17^3 + 18^3 + 19^3), then x divided by 70 leaves a remainder of<\/strong><\/p>\n

1) 0
\n2) 1
\n3) 69
\n4) 35<\/p>\n

Remark<\/strong> : It uses concept of previous questions, but it has 1 extra condition to remember.<\/p>\n

Solution here:<\/strong>\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226247444209622\/<\/a><\/p>\n

4. Let n! = 1 \u00d7 2 \u00d7 3 \u00d7 … \u00d7 n for integer n \u2265 1. If p = 1! + (2 \u00d7 2!) + (3 \u00d7 3!) + \u2026 +(10 \u00d7 10!), then p + 2 when divided by 11! leaves a remainder of<\/strong><\/p>\n

1) 10
\n2) 0
\n3) 7
\n4) 1<\/p>\n

Remark :<\/strong> It has 2 ways : One by general expanding and other is a generalised shortcut, both discussed in the link below<\/p>\n

Solution here:\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226255684208798\/<\/a><\/strong><\/p>\n

5. Let N = 1421 \u00d7 1423 \u00d7 1425. What is the remainder when N is divided by 12?<\/strong><\/p>\n

1) 0
\n2) 9
\n3) 3
\n4) 6<\/p>\n

Remark :<\/strong> It is one of the easiest questions on remainder asked in CAT.<\/p>\n

Solution here<\/strong>:\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226268600874173\/<\/a><\/p>\n

6. The integers 34041 and 32506 when divided by a three-digit integer \u2018n\u2019 leave the same remainder. What is \u2018n\u2019?<\/strong><\/p>\n

Remark :<\/strong> It is a very conceptual question and tricky one if one doesn’t know the solution already.<\/p>\n

Solution here :<\/strong>\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226277290873304\/<\/a><\/p>\n

7. On dividing a number by 3, 4 and 7, the remainders are 2, 1 and 4 respectively. If the same number is divided by 84 then the remainder is<\/strong><\/p>\n

1) 80
\n2) 76
\n3) 53
\n4) None of these<\/p>\n

Remark :<\/strong> A question on Chinese remainder theorem<\/p>\n

Solution here:<\/strong>\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226287320872301\/<\/a><\/p>\n

8. For all integers n > 0, 7^6n \u2013 6^6n is divisible by<\/strong><\/p>\n

1) 13
\n2) 127
\n3) 559
\n4) All of these<\/p>\n

Remark:<\/strong> An application of algebraic formula a^2-b^2=(a-b)(a+b)<\/p>\n

Solution here:<\/strong>\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226297767537923\/<\/a><\/p>\n

9. The remainder when 2^256 is divided by 17 is<\/strong><\/p>\n

1) 7
\n2) 13
\n3) 11
\n4) 1<\/p>\n

Remark :<\/strong> A simple question on Euler theorem<\/p>\n

Solution here:<\/strong>\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226305060870527\/<\/a><\/p>\n

10. 101! Mod 103 [ CAT 2003]<\/strong><\/p>\n

Remark :<\/strong> A simple question on Wilson Theorem<\/p>\n

Solution here :\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1226308500870183\/<\/a><\/strong><\/p>\n

\u25cf CAT 20 Course Details:\u00a0https:\/\/www.facebook.com\/groups\/Rockthecat\/permalink\/1182586281909072\/<\/a><\/strong><\/p>\n

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