List of top Questions asked in XAT- 2007

DIRECTIONS for questions 78 to 81: Read the data below and choose the correct option for the questions that follow.

Queen Airlines offers the following Privilege programme: there are 5 membership tiers, each with its own set of enhanced tier-specific benefits. New members join at the Blue tier, then upgrade to Blue Plus, which adds the benefit of Tele check-in. The programme also has three elite tiers, Silver, Gold and Platinum. The 6-month fast-track upgrade and the 12-month standard upgrade system work in parallel: whenever a passenger meets the condition for the next tier, either in terms of the number of flights taken in the stipulated period or in terms of accumulated Queen-Miles, in either of the two systems, the passenger is automatically upgraded to the next tier. The 6-month system looks at a rolling 6-month period, and the 12-month system looks at a rolling 12-month period. If conditions for more than one upgrade are met at the same time, the passenger is given the higher of the two tiers.

Tier Upgrade6-month Fast Track Upgrade System
(Cumulative flights / Cumulative Queen-Miles)		12-month Standard Upgrade System
(Cumulative flights / Cumulative Queen-Miles)
Blue to Blue Plus3 / 3,000Not Applicable
Blue Plus to SilverNot Applicable5 / 12,500
Silver to Gold5 / 12,50010 / 20,000
Gold to Platinum10 / 20,00020 / 30,000

Benefits and Privileges

BlueBlue PlusSilverGoldPlatinum
Tele Check-in✓✓✓✓
Additional baggage allowance10 kgs20 kgs35 kgs
Confirmed upgrade vouchers135
Guaranteed reservations upto 24 hours prior to departure✓✓
Cancellation fees waived on published fares✓

Distances between cities in Queen-miles

DelhiKolkataMumbaiHyderabadBangaloreCoimbatoreGuwahati
Kolkata1461
Mumbai14071987
Hyderabad14991516711
Bangalore20611881998562
Coimbatore240121671265902340
Guwahati195910812746237029323209
Chennai2095167613296883314912718

Mr Kakkar, a newly recruited MBA from a business school, started his career at the start of 2007. His travel plan for 2007 is given below.

DateFromTo
2.1.2007MumbaiHyderabad
8.1.2007HyderabadMumbai
3.2.2007MumbaiDelhi
8.3.2007DelhiGuwahati
20.3.2007GuwahatiKolkata
11.4.2007KolkataGuwahati
30.4.2007GuwahatiChennai
4.7.2007ChennaiGuwahati
20.7.2007GuwahatiKolkata
2.9.2007KolkataHyderabad
11.9.2007HyderabadGuwahati
22.9.2007GuwahatiDelhi
1.10.2007ChennaiBangalore
11.10.2007GuwahatiChennai
4.11.2007ChennaiDelhi
29.11.2007DelhiHyderabad
1.12.2007HyderabadGuwahati
31.12.2007GuwahatiMumbai

The difference in complete calendar months, discounting any partial months, between the first tier upgrade and the last tier upgrade for Mr Kakkar is:

ABC is a triangle with \(\angle BAC = 60^{\circ}\). A point P lies on one-third of the way from B to C, and AP bisects \(\angle BAC\). \(\angle APC = ?\)

DIRECTIONS for questions 78 to 81: Read the data below and choose the correct option for the questions that follow.

Queen Airlines offers the following Privilege programme: there are 5 membership tiers, each with its own set of enhanced tier-specific benefits. New members join at the Blue tier, then upgrade to Blue Plus, which adds the benefit of Tele check-in. The programme also has three elite tiers, Silver, Gold and Platinum. The 6-month fast-track upgrade and the 12-month standard upgrade system work in parallel: whenever a passenger meets the condition for the next tier, either in terms of the number of flights taken in the stipulated period or in terms of accumulated Queen-Miles, in either of the two systems, the passenger is automatically upgraded to the next tier. The 6-month system looks at a rolling 6-month period, and the 12-month system looks at a rolling 12-month period. If conditions for more than one upgrade are met at the same time, the passenger is given the higher of the two tiers.

Tier Upgrade6-month Fast Track Upgrade System
(Cumulative flights / Cumulative Queen-Miles)		12-month Standard Upgrade System
(Cumulative flights / Cumulative Queen-Miles)
Blue to Blue Plus3 / 3,000Not Applicable
Blue Plus to SilverNot Applicable5 / 12,500
Silver to Gold5 / 12,50010 / 20,000
Gold to Platinum10 / 20,00020 / 30,000

Benefits and Privileges

BlueBlue PlusSilverGoldPlatinum
Tele Check-in✓✓✓✓
Additional baggage allowance10 kgs20 kgs35 kgs
Confirmed upgrade vouchers135
Guaranteed reservations upto 24 hours prior to departure✓✓
Cancellation fees waived on published fares✓

Distances between cities in Queen-miles

DelhiKolkataMumbaiHyderabadBangaloreCoimbatoreGuwahati
Kolkata1461
Mumbai14071987
Hyderabad14991516711
Bangalore20611881998562
Coimbatore240121671265902340
Guwahati195910812746237029323209
Chennai2095167613296883314912718

Mr Kakkar, a newly recruited MBA from a business school, started his career at the start of 2007. His travel plan for 2007 is given below.

DateFromTo
2.1.2007MumbaiHyderabad
8.1.2007HyderabadMumbai
3.2.2007MumbaiDelhi
8.3.2007DelhiGuwahati
20.3.2007GuwahatiKolkata
11.4.2007KolkataGuwahati
30.4.2007GuwahatiChennai
4.7.2007ChennaiGuwahati
20.7.2007GuwahatiKolkata
2.9.2007KolkataHyderabad
11.9.2007HyderabadGuwahati
22.9.2007GuwahatiDelhi
1.10.2007ChennaiBangalore
11.10.2007GuwahatiChennai
4.11.2007ChennaiDelhi
29.11.2007DelhiHyderabad
1.12.2007HyderabadGuwahati
31.12.2007GuwahatiMumbai

If 6-month upgrade had not been in operation, then Mr Kakkar would have reached the Gold tier in the month of:

DIRECTIONS for questions 82 and 83: The graph below gives the number of electronic commerce transactions that took place in the last six months of financial year 2005. This graph shows data for private consumption only and does not include corporate electronic commerce activity. The numbers above each bar are in millions, and the average price per unit for each product category is shown in brackets in the legend.

For which product category is the revenue contribution of the Asia Pacific region the maximum?

For which value of non-negative 'a' will the system \(x^2 - y^2 = 0\), \((x-a)^2 + y^2 = 1\) have exactly three real solutions?
Directions: Each of the following questions is followed by two statements, labelled (A) and (B). Decide whether the statements are sufficient to conclusively answer the question, and choose:
(A) if Statement (A) alone is sufficient but Statement (B) alone is not.
(B) if Statement (B) alone is sufficient but Statement (A) alone is not.
(C) if Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
(D) if either Statement (A) alone or Statement (B) alone is sufficient.
(E) if both statements together are still not sufficient.

ABC is a triangle with \(\angle B = 90^{\circ}\). What is the length of the side AC?
(A) D is the midpoint of BC and E is the midpoint of AB.
(B) AD = 7 and CE = 5.
Directions: Each of the following questions is followed by two statements, labelled (A) and (B). Decide whether the statements are sufficient to conclusively answer the question, and choose:
(A) if Statement (A) alone is sufficient but Statement (B) alone is not.
(B) if Statement (B) alone is sufficient but Statement (A) alone is not.
(C) if Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
(D) if either Statement (A) alone or Statement (B) alone is sufficient.
(E) if both statements together are still not sufficient.

Let \(f : N \to N\) (N is the set of all natural numbers). How many solutions are there to the equation \(f(x) = 1485\)?
(A) For \(a, b \in N\), \(f(10a+b) = f(a) + 12b\).
(B) The maximum value of b is 9.
Directions: Each of the following questions is followed by two statements, labelled (A) and (B). Decide whether the statements are sufficient to conclusively answer the question, and choose:
(A) if Statement (A) alone is sufficient but Statement (B) alone is not.
(B) if Statement (B) alone is sufficient but Statement (A) alone is not.
(C) if Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
(D) if either Statement (A) alone or Statement (B) alone is sufficient.
(E) if both statements together are still not sufficient.

Five integers A, B, C, D and E are arranged in such a way that there are two integers between B and C, and B is not the greatest. There exists one integer between D and E, and D is smaller than E. A is not the smallest integer. Which one is the smallest?
(A) E is the greatest.
(B) There exists no integer between B and E.
Let \(\{A_n\}\) be a unique sequence of positive integers satisfying the following properties: \(A_1 = 1,\ A_2 = 2,\ A_4 = 12\), and \(A_{n+1}\cdot A_{n-1} = A_n^2 \pm 1\) for \(n = 2, 3, 4, \dots\)
Then, \(A_7\) is:
Directions for questions 67 to 70: Seven integers A, B, C, D, E, F and G are to be arranged in increasing order such that:
(i) The first four numbers, in this increasing order, are in arithmetic progression (A.P.).
(ii) The last four numbers, in this increasing order, are in geometric progression (G.P.).
(iii) There is exactly one number between E and G, in the increasing order.
(iv) There is no number between A and B, in the increasing order.
(v) D is the smallest number and E is the greatest number.
(vi) \[ \frac{A}{D}=\frac{G}{C}=\frac{F}{A}>1 \]
(vii) E = 960

69. The common difference in the A.P. is:
Directions for questions 67 to 70: Seven integers A, B, C, D, E, F and G are to be arranged in increasing order such that:
(i) The first four numbers, in this increasing order, are in arithmetic progression (A.P.).
(ii) The last four numbers, in this increasing order, are in geometric progression (G.P.).
(iii) There is exactly one number between E and G, in the increasing order.
(iv) There is no number between A and B, in the increasing order.
(v) D is the smallest number and E is the greatest number.
(vi) \[ \frac{A}{D}=\frac{G}{C}=\frac{F}{A}>1 \]
(vii) E = 960

68. D = ?
Directions: Each of the following questions is followed by two statements, labelled (A) and (B). Decide whether the statements are sufficient to conclusively answer the question, and choose:
(A) if Statement (A) alone is sufficient but Statement (B) alone is not.
(B) if Statement (B) alone is sufficient but Statement (A) alone is not.
(C) if Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
(D) if either Statement (A) alone or Statement (B) alone is sufficient.
(E) if both statements together are still not sufficient.

What is the maximum value of a/b?
(A) a, a + b and a + 2b are three sides of a triangle.
(B) a and b both are positive.
Directions: Seven integers A, B, C, D, E, F and G are to be arranged in increasing order such that:
(i) The first four numbers (in this increasing order) are in arithmetic progression.
(ii) The last four numbers (in this increasing order) are in geometric progression.
(iii) There is exactly one number between E and G.
(iv) There is no number between A and B.
(v) D is the smallest number and E is the greatest.
(vi) \( \dfrac{A}{D} = \dfrac{G}{C} = \dfrac{F}{A} > 1 \)
(vii) E = 960

The position and value of A is:
Directions for questions 67 to 70: Seven integers A, B, C, D, E, F and G are to be arranged in increasing order such that:
(i) The first four numbers, in this increasing order, are in arithmetic progression (A.P.).
(ii) The last four numbers, in this increasing order, are in geometric progression (G.P.).
(iii) There is exactly one number between E and G, in the increasing order.
(iv) There is no number between A and B, in the increasing order.
(v) D is the smallest number and E is the greatest number.
(vi) \[ \frac{A}{D}=\frac{G}{C}=\frac{F}{A}>1 \]
(vii) E = 960

67. \(\dfrac{E}{A} = ?\)
66. A management institute has six senior professors and four junior professors. Three professors are selected at random for a government project. The probability that at least one of the junior professors would get selected is:

Directions for questions 62 and 64: Substitute different digits (0, 1, 2, ... 9) for different letters in the problem below, so that the corresponding addition is correct and it results in the maximum possible value of MONEY.

PAY
ME
REAL
MONEY

This grid represents the addition PAY + ME + REAL = MONEY, where each letter stands for exactly one digit and no two letters share the same digit.

The letter 'Y' should be:

65. Consider the system of linear equations:
\[ 2x + 3y + 4z = 16 \]
\[ 4x + 4y + 5z = 26 \]
\[ ax + by + cz = r \]
For \(r = 5\) and \(a = 1\), the system of linear equations will have an infinite number of solutions if \(c = ?\)
Directions for questions 63 and 64: Substitute different digits (0 to 9) for different letters in the addition below, so that the addition is correct and it gives the maximum possible value of MONEY.
PAY
ME
REAL
MONEY
So the addition reads PAY + ME + REAL = MONEY, using nine different letters: P, A, Y, M, E, R, L, O, N.

64. The resulting value of 'MONEY' is:
Directions for questions 63 and 64: Substitute different digits (0 to 9) for different letters in the addition below, so that the addition is correct and it gives the maximum possible value of MONEY.
PAY
ME
REAL
MONEY
So the addition reads PAY + ME + REAL = MONEY, using nine different letters: P, A, Y, M, E, R, L, O, N.

63. There are nine letters and ten digits. The digit that remains unutilized is:
Let a, b, c, d and e be non-negative real numbers such that a + b + c + d + e = 10. Let X be the maximum of the numbers a + b, b + c, c + d and d + e. The least possible value of X lies in the interval:
In a rainy season, Jamshedpur experienced some rain for thirteen days. A morning rain was always followed by a clear evening. An evening rain was always preceded by a clear morning. A total of 9 mornings and 12 evenings were clear. How many rainless days did Jamshedpur have in the period?
A brokerage house offers 3 stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds and 3 blocks of preferred stock. Portfolio III consists of 2 blocks of common stock, 2 municipal bonds and 3 blocks of preferred stock. A customer wants 12 blocks of common stock, 6 municipal bonds and 6 preferred stocks. How many portfolio III should be offered?
Triangle ABC has vertices A(0, 0), B(0, 6) and C(9, 0). The points P and Q lie on side AC such that AP = PQ = QC. Similarly, the points R and S lie on side AB such that AR = RS = SB. If the line segments PB and RC intersect at X, then the slope of the line AX is:
ABCD is a rectangle. The points P and Q lie on AD and AB respectively. If the triangles PAQ, QBC and PCD all have the same areas and BQ = 2 then AQ = ?
In a certain factory, each day the expected number of accidents is related to the number of overtime hours by a linear equation. Suppose that on one day there were 1000 overtime hours logged and 8 accidents reported, and on another day there were 400 overtime hours logged and 5 accidents. What are the expected numbers of accidents when no overtime hours are logged?