In economics, if a diagram has a line passing through the origin and has 45° angle with either axis and it is asserted that along the line X = Y, what is tacitly assumed?
- (a)Both variables are pure numbers.
- (b)Both variables are in the same unit.
- (c)Both variables are in different units.
- (d)At least one variable is a pure number.
Correct — B, Both variables are in the same unit. The line described runs through the origin at forty-five degrees to both axes, so at every point on it the horizontal distance from the origin equals the vertical distance. Reading that as X = Y is a step beyond geometry: it says the two measurements are equal as quantities, and a quantity can only equal another if the two are measured in the same unit. Suppose X is a length in metres and Y a weight in kilograms — the point six metres, six kilograms lies on the line, but nothing meaningful has been asserted by writing six metres equals six kilograms. Same unit is what the equality quietly presupposes, and that presupposition is the tacit assumption the question is asking for. A further condition hides underneath it: both axes must also be drawn to the same scale, or the equal-quantity line would not come out at forty-five degrees.
- (a)Both variables are pure numbers. — Sufficient but stronger than the question needs. Pure numbers are one way of being in the same unit — the dimensionless case — but two variables can both be in rupees, or both in tonnes, and X = Y still reads perfectly well. The assumption being made is the weaker and more general one.
- (c)Both variables are in different units. — The exact opposite of what the equality requires. If the units differ, the statement X = Y has no content, and the forty-five degree line would carry no economic meaning at all.
- (d)At least one variable is a pure number. — Neither necessary nor sufficient. Two variables both measured in rupees satisfy the equality with neither being a pure number, and one pure number paired with a variable in metres still leaves the equality meaningless.
A forty-five degree line through the origin is one of the standard devices of economic diagrams. In the Keynesian cross it marks the points where planned expenditure equals income; in a Lorenz curve diagram it is the line of perfect equality; in a two-good consumption diagram it marks equal quantities of the two goods. Every one of those readings depends on both axes being measured in the same unit and drawn to the same scale.
The item is a small test of dimensional discipline dressed up as a diagram question. Work it as a logic problem: which of the four statements must be true for X = Y to mean anything? Option (a) would make it true, but is not required; options (c) and (d) make it worse or leave it unfixed. Only (b) is both necessary and enough. A note on the paper itself, since the answer here does not depend on any figure: the bank flags this question as carrying an image, but the printed booklet does not show one. Page 17 of the Series A booklet carries Q53 in the left-hand column with the stem and four options and nothing else — no diagram, no axes, no line. The question is fully answerable from the words, which is what the wording is designed to do; it describes the diagram rather than showing it.
- A line through the origin at forty-five degrees to both axes has equal horizontal and vertical coordinates at every point.
- Writing X = Y for such a line asserts equality of quantities, which requires both to be in the same unit.
- Both axes must also be drawn to the same scale for the equal-quantity line to appear at forty-five degrees.
- Being a pure number is one special case of being in the same unit, not a requirement.
- The forty-five degree line is the equality line of a Lorenz diagram and the planned-expenditure-equals-income line of the Keynesian cross.
The printed booklet carries no figure for this question; the stem describes the diagram in words.
- Choosing the strongest-sounding option; pure numbers would work but are not what the equality assumes.
- Forgetting that the scale of the two axes, not just the unit, is what puts the line at forty-five degrees.
As a reasoning item on what a described diagram presupposes, or as a Lorenz curve or Keynesian cross question in economics.
No directly related past PYQ was found.
- practice — not a real PYQ
In a Lorenz curve diagram, the straight line drawn from the origin at forty-five degrees represents
- (a)perfect inequality of income
- (b)perfect equality of income
- (c)the poverty line
- (d)the average income
Answer(b) perfect equality of income — on that line each cumulative share of the population receives exactly the same cumulative share of income.
- practice — not a real PYQ
In the Keynesian cross diagram, the forty-five degree line shows all the points at which
- (a)saving equals investment by definition
- (b)planned expenditure equals income
- (c)the price level is constant
- (d)the money market clears
Answer(b) planned expenditure equals income — equilibrium is where the expenditure schedule cuts that line.