Download Puzzles Questions for CAT<\/a><\/p>\n CAT Online Coaching<\/a><\/p>\n Question 1:\u00a0<\/b>In a family gathering there are 2 males who are grandfathers and 4 males who are fathers. In the same gathering there are 2 females who are grandmothers and 4 females who are mothers. There is at least one grandson or a granddaughter present in this gathering. There are 2 husband-wife pairs in this group. These can either be a grandfather and a grandmother, or a father and a mother. The single grandfather (whose wife is not present) has 2 grandsons and a son present. The single grandmother (whose husband is not present) has 2 grand daughters and a daughter present. A grandfather or a grandmother present with their spouses does not have any grandson or granddaughter present. What is the minimum number of people present in this gathering?<\/p>\n a)\u00a010<\/p>\n b)\u00a012<\/p>\n c)\u00a014<\/p>\n d)\u00a016<\/p>\n 1)\u00a0Answer\u00a0(B)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n The bare minimum requirement for the single grandfather and grandmother are as follows:<\/p>\n GF implies Grandfather, GM Grandmother, F Father, M Mother, GS Grandson and GD Granddaughter. The family trees above account for 2 fathers, 2 mothers, 1 GF and 1 GM. Hence, we need 1 more GF, 1 GM, 2 fathers and 2 mothers and two married couples.<\/p>\n The bare minimum tree that would provide this structure is as follows:<\/p>\n Using these three structures, we have fit all of our requirements. Thus, if GF1, GF2 and GM1 are siblings with the following family trees present, we would have the required number of people in attendance. Hence, the minimum is 12 people.<\/p>\n Question 2:\u00a0<\/b>A calculator has two memory buttons, A and B. Value 1 is initially stored in both memory locations. The following sequence of steps is carried out five times: a)\u00a0120<\/p>\n b)\u00a0450<\/p>\n c)\u00a0720<\/p>\n d)\u00a0250<\/p>\n 2)\u00a0Answer\u00a0(C)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n A calculator has two memory buttons, A and B. Value 1 is initially stored in both memory locations. The following sequence of steps is carried out five times: The value in A and B before the start of the process is 1 and 1 respectively. In 2nd iteration, In 3rd iteration, In 4th iteration, In 5th iteration, Hence, option D is the correct answer.<\/p>\n Instructions<\/b><\/p>\n A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence. Question 3:\u00a0<\/b>The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not. 3)\u00a0Answer:\u00a011<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Let the original sequence be TIMRL<\/p>\n Two fingers can be out of place. This can be done if and only if two fingers interchange their position. These two can be selected in $^5C_2 = 10$ ways. In addition to these, the original sequence will also be accepted. Hence the total number of acceptable sequences = 10 + 1 = 11<\/p>\n Question 4:\u00a0<\/b>The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is also allowed, but LIMRT is not. a)\u00a07<\/p>\n b)\u00a05<\/p>\n c)\u00a08<\/p>\n d)\u00a013<\/p>\n 4)\u00a0Answer\u00a0(C)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. This can be achieved only when two consecutive fingers are interchanged. Let the original sequence be TIMRL Including the original sequence, we get the total number of allowed combinations as 8<\/p>\n Question 5:\u00a0<\/b>The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL. 5)\u00a0Answer:\u00a015<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n There can be two scans out of place.<\/p>\n TIMTRL is the original sequence.<\/p>\n If T is interchanged: There will be four ways: ITMTRL, MITTRL, RIMTTL, LIMTRT<\/p>\n If I is interchanged: There will be four ways<\/p>\n If M is interchanged: There will be three ways<\/p>\n If T is interchanged: There will be two ways<\/p>\n If R is interchanged: There will be one way<\/p>\n Total 14.<\/p>\n Another sequence allowed is original, So total 15 ways.<\/p>\n Question 6:\u00a0<\/b>The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL. a)\u00a08<\/p>\n b)\u00a011<\/p>\n c)\u00a013<\/p>\n d)\u00a014<\/p>\n 6)\u00a0Answer\u00a0(C)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n 1. If original sequence is given.<\/p>\n 2. If either of LR, RL, LT, TI, IM is interchanged => 5 ways.<\/p>\n 3. If LR and LT and IM interchanged. The sequence will look like: RLTLMI<\/p>\n 4. If LR and LT are interchanged.<\/p>\n 5. If LR and TI are interchanged.<\/p>\n 6. If LR and IM are interchanged.<\/p>\n 7. If RL and TI are interchanged.<\/p>\n 8. If RL and IM\u00a0 are interchanged.<\/p>\n 9. If LT and IM are interchanged.<\/p>\n Total 13 ways possible.<\/p>\n Instructions<\/b><\/p>\n Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun,\u00a0Chetan, and Deb are four male students. Each of them studies in one of three institutes – X, Y, and Z. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:<\/p>\n 1. Three students are from X, three are from Y, and the remaining two students, both female, are from Z. Question 7:\u00a0<\/b>Who are the students from the institute Z?<\/p>\n a)\u00a0Chitra and Daisy<\/p>\n b)\u00a0Adriana and Bandita<\/p>\n c)\u00a0Bandita and Chitra<\/p>\n d)\u00a0Adriana and Daisy<\/p>\n 7)\u00a0Answer\u00a0(C)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n There are 8 students in total – 4 male and 4 female. There are 3 institutes X, Y, and Z. It has been given that both the students from institute Z are female. Also, it has been given that both the male students from institute Y minor in Finance. Therefore, the third student from institute Y should be female. Institute X should also have 2 male and 1 female student.<\/p>\n Both\u00a0the male students from Y minor in Finance, while the female student from Y majors in Operations.\u00a0Barun is from Y and majors in Operations. Chetan is from X and majors in Finance.<\/p>\n It has been given that one female student and 2 male students major in finance. We know that the male student from Y minors in finance. Therefore, he cannot major in finance. Therefore, both the male students from X should major in finance.<\/p>\n Daisy and Amit are from the same institute. Therefore,\u00a0Daisy cannot be from institute Z (since Amit is a male student and both the students from\u00a0Z are female). Daisy minors in operations. The girl from institute Y majors in Operations. Therefore, Daisy cannot be from institute Y as well. Daisy and Amit should be from institute X. 3 female students minor in marketing. Therefore, all girls except Daisy should minor in marketing.<\/p>\n Adriana and Deb are from the same institute. Therefore, both of them should be from institute Y. Bandita and Chitra should be from institute Z.<\/p>\n Only one male student majors in Operations. We know that Barun is the student. Two male students major in Finance. We know that Amit and Chetan major in finance. Therefore, Deb should major in Marketing.<\/p>\n Bandita and Chitra are from institute Z. Therefore, option C is the right answer.<\/p>\n Question 8:\u00a0<\/b>Which subject does Deb minor in?<\/p>\n a)\u00a0Operations<\/p>\n b)\u00a0Finance<\/p>\n c)\u00a0Marketing<\/p>\n d)\u00a0Cannot be determined uniquely from the given information<\/p>\n 8)\u00a0Answer\u00a0(B)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n There are 8 students in total – 4 male and 4 female. There are 3 institutes X, Y, and Z. It has been given that both the students from institute Z are female. Also, it has been given that both the male students from institute Y minor in Finance. Therefore, the third student from institute Y should be female. Institute X should also have 2 male and 1 female student.<\/p>\n Both\u00a0the male students from Y minor in Finance, while the female student from Y majors in Operations.\u00a0Barun is from Y and majors in Operations. Chetan is from X and majors in Finance.<\/p>\n It has been given that one female student and 2 male students major in finance. We know that the male student from Y minors in finance. Therefore, he cannot major in finance. Therefore, both the male students from X should major in finance.<\/p>\n Daisy and Amit are from the same institute. Therefore,\u00a0Daisy cannot be from institute Z (since Amit is a male student and both the students from\u00a0Z are female). Daisy minors in operations. The girl from institute Y majors in Operations. Therefore, Daisy cannot be from institute Y as well. Daisy and Amit should be from institute X. 3 female students minor in marketing. Therefore, all girls except Daisy should minor in marketing.<\/p>\n Adriana and Deb are from the same institute. Therefore, both of them should be from institute Y. Bandita and Chitra should be from institute Z.<\/p>\n Only one male student majors in Operations. We know that Barun is the student. Two male students major in Finance. We know that Amit and Chetan major in finance. Therefore, Deb should major in Marketing.<\/p>\n Deb minors in Finance. Therefore, option\u00a0B is the right answer.<\/p>\n Question 9:\u00a0<\/b>Which subject does Amit major in?<\/p>\n a)\u00a0Marketing<\/p>\n b)\u00a0Operations<\/p>\n c)\u00a0Cannot be determined uniquely from the given information<\/p>\n d)\u00a0Finance<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/img1_SFKrDOx.png\")
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\nadd 1 to B
\nmultiply A to B
\nstore the result in A
\nWhat is the value stored in memory location A after this procedure?<\/p>\n
\nadd 1 to B
\nmultiply A to B
\nstore the result in A
\nWhat is the value stored in memory location A after this procedure?<\/p>\n
\nIn 1st iteration,
\nAfter step I, A = 1 and B = 2
\nAfter steps II and III, A = 1 * 2 = 2, B = 2<\/p>\n
\nAfter step I, A = 2 and B = 3
\nAfter steps II and III, A = 2 * 3 = 6, B = 3<\/p>\n
\nAfter step I, A = 6 and B = 4
\nAfter steps II and III, A = 6 * 4 = 24, B = 4<\/p>\n
\nAfter step I, A = 24 and B = 5
\nAfter steps II and III, A = 24 * 5 = 120, B = 5<\/p>\n
\nAfter step I, A = 120 and B = 6
\nAfter steps II and III, A = 120 * 6 = 720, B = 6<\/p>\n
\nThe lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.<\/p>\n
\nHow many different sequences of scans are allowed for any given person’s original scan?<\/p>\n
\nHow many different sequences are allowed for any given person’s original scan?<\/p>\n
\nCase 1: Only a set of two consecutive numbers are interchanged.
\nThey can be selected in 5-1 = 4 ways
\nCase 2: Two sets of two consecutive numbers are interchanged.
\n(i) TI are interchanged, => (MR, RL) => 2 ways
\n(ii) IM are interchanged => (RL) => 1 way
\nTotal no of ways possible = 4 + 2 + 1 = 7<\/p>\n
\nSuppose the lab allows a variation of the original sequence (of six inputs) where at most two scans (out of six) are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
\nHow many different sequences of scans are allowed for any given person’s original scan?<\/p>\n
\nSuppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
\nHow many different sequences of scans are allowed if the original scan sequence is LRLTIM?<\/p>\n
\n2. Both the male students from Y minor in Finance, while the female student from Y majors in Operations.
\n3. Only one male student majors in Operations, while three female students minor in Marketing.
\n4. One female and two male students major in Finance.
\n5. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
\n6. Barun is from Y and majors in Operations. Chetan is from X and majors in Finance.
\n7. Daisy minors in Operations.<\/p>\n
\n3 students are from institute X, 3 students are from institute Y, and 2 students are from institute Z. No student majors and minors in the same subject.<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/M1.JPG\")
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\n3 students are from institute X, 3 students are from institute Y, and 2 students are from institute Z. No student majors and minors in the same subject.<\/p>\n<\/figure>\n<\/figure>\n<\/figure>\n<\/figure>\n